Free Printable Unit 5 – Trig Functions - Radian

1.

We start things with a....

a)

BANG

b)

BANG

c)

BANG

d)

BANG

2.

True or False: Regular Sine is a one to one function.

a)

True

b)

False

3.

A ---- function is a function that maps no two elements of its domain to a single value in its range

a)

one to one

b)

inverse

4.

What is the domain of a restricted sine?

a)

$\left(-\frac{\pi}{2},\ \frac{\pi}{2}\right)$

b)

$\left(-1,1\right)$

5.

What is the range of restricted sine?

a)

$\left(-\frac{\pi}{2},\ \frac{\pi}{2}\right)$

b)

(-1,1)

6.

$f^{-1}\left(f\left(x\right)\right)=\sin^{-1}\left(\sin x\right)=x\$ than has a restriction of

a)

$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

b)

$-1\le x\le1$

7.

$f\left(f^{-1}\left(x\right)\right)=\sin\left(\sin^{-1}x\right)=x\$ has a restriction at

a)

$-\frac{\pi}{2}\le x\le\frac{\pi}{2}$

b)

$-1\le x\le1$

8.

How should $y=\sin^{-1}x$ be also written

a)

$x=\sin y\$

b)

$y=\sin x\$

9.

When finding the exact values for certain composite functions such as Sine, and it exceeds the radians, what can one do?

a)

Use the reference angle

b)

Use The angle given that exceeds the limit

10.

What is the domain of cosine that is one to one?

a)

$0\le x\le\pi$

b)

$-1\le x\le1$

11.

What is the range of cosine function?

a)

$-1\le x\le1$

b)

$0\le x\le\pi$

12.

$f^{-1}\left(f\left(x\right)\right)=\cos^{-1}\left(\cos\left(x\right)\right)=x$ What restriction would this have?

a)

$0\le x\le\pi$

b)

$-1\le x\le1$

13.

Cosine is

a)

odd

b)

even

14.

Sine is

a)

even

b)

odd

15.

$f\left(f^{-1}\left(x\right)\right)=\cos\left(\cos^{-1}x\right)=x\$ restriction occurs

a)

$0\le x\le\pi$

b)

$-1\le x\le1$

16.

$y=\tan^{-1}x$

a)

$x=\tan y$

b)

$y=\tan x$

17.

What restriction does this have $f^{-1}\left(f\left(x\right)\right)=\tan^{-1}\left(\tan\left(x\right)\right)=x$

a)

$-\frac{\pi}{2}\le x\le\frac{\pi}{2}$

b)

$-\infty\le x\le\infty$

18.

What is the restriction of this $f\left(f^{-1}\left(x\right)\right)=\tan\left(\tan^{-1}x\right)=x$

a)

$\frac{-\pi}{2}\le x\le\frac{\pi}{2}$

b)

$-\infty\le x\le\infty$

19.

What is the first step finding inverse of a trig function

a)

Switch X and Y

b)

Solve For Y

c)

Do Inverse Operations

20.

What is the second step to finding the inverse function of a trig function?

a)

Make sure y is alone with the sine

b)

Solve X and Y

c)

Switch X and Y

21.

True or False: Reference angle can be negative and Positive

a)

True

b)

False

22.

What must the new angle found from the followed angle be

a)

The same sign

b)

Follow the restrictions of the trig

c)

Be total of 360 degrees

d)

Be the same distance from the x-axis from the reference angle

23.

$\sin\left(x\right)\$ is really

a)

y(ratio)

b)

x(angle)

24.

$\sin^{-1}\left(x\right)$ is really

a)

y(ratio)

b)

x(angle)

25.

When asked to find the exact value of $\sin\left(\tan^{-1}\left(\frac{1}{2}\right)\right)$ what should one do?

a)

Find the angle of the inside

b)

Find the restriction of the domain of the inner function.

c)

Find the entire triangle to than find sine ratio

26.

True or False: Follow the restriction given for the inner functions of an expression

a)

True

b)

False

27.

What is sec domain

a)

$0\le x\le\pi$

b)

$\left|x\right|\ge1$

c)

x $y\ne\frac{\pi}{2}$

28.

Find the range of sec(x)

a)

$0\le y\le\pi$

b)

$\left|y\right|\ge1$

c)

$y\ne\frac{\pi}{2}$

29.

The domain and range of inverse trig functions....

a)

stay the same

b)

switch from their inverses

c)

only sine and cosecant switch

30.

What is the domain of csc(x)

a)

$-\frac{\pi}{2}\le x\le\frac{\pi}{2}$

b)

$0<y<\pi$

c)

$0\le y\le\pi$

d)

$y\ne0$

e)

$y\ge0$

31.

The range of csc(x) is also known as

a)

$\left|y\right|\ge1$

b)

$\left|y\right|\le1$

32.

What is the domain of cot(x)

a)

$0<x<0$

b)

$0\le x\le\pi$

c)

$0<x<\pi$

33.

What is the range of cot(x)

a)

$-\infty\le x<\infty$

b)

$-\infty\le x\le\infty$

c)

$-\infty<x<\infty$

34.

X is often known in trig functions as the

a)

domain

b)

the angle

c)

ratio

35.

Y is often known as

a)

ratio

b)

angle

36.

True or False: Finding the inverse of secant and cotangent can both use cosine

a)

True, Inverse of Secant and Cotangent share the same domain of cosine. Both are reciprocals of cosine, therefore just flipping them will do!

b)

True, Inverse of secant and cotangent share the same domain of cosine, however secant is just the reciprocal of cosine. Cotangent must give the correct sides to than evaluate with cosine

37.

Cotangent works in which quadrants?

a)

1

b)

2

c)

3

d)

4

38.

Which quadrants does tangent work in?

a)

1

b)

2

c)

3

d)

4

39.

Cosecant works in which side?

a)

1

b)

2

c)

3

d)

4

40.

Secant Works In this Side

a)

1

b)

2

c)

3

d)

4

41.

Cosine works in this side

a)

1

b)

2

c)

3

d)

4

42.

Sine works in this side

a)

1

b)

2

c)

3

d)

4

43.

Cosecant Works in Which One?

a)

1

b)

2

c)

3

d)

4

44.

Writing a trigonometric Expression is the same as finding the exact value of an Inverse Cosecant Function, except....

a)

There is no except, keep using them numbers!

b)

This time we are using variables to draw out these ratios!

45.

Quizizz AI returned better and stronger! How should we celebrate?!

a)

Ignore the achievement and move on.

b)

Post a meme about it on social media.

c)

Send an email to all users about the update.

d)

Host a virtual celebration event.

46.

Welecome back Quizizz AI to my math learning, how are you better than human made questions and concept questions?

a)

Quizizz AI is better at generating diverse and adaptive questions.

b)

Quizizz AI cannot adapt to different learning styles.

c)

Human-made questions are always more accurate.

d)

Quizizz AI only repeats existing questions.

47.

There is infinite amount of solutions for trig functions if there ins't a limit

a)

There are only two solutions for trig functions without limits.

b)

Trigonometric functions have a finite number of solutions.

c)

All trig functions have a unique solution without limits.

d)

True, there are infinite solutions for trig functions without limits.

48.

$k\in Z$ What do the k the middle part and Z mean

a)

k is an integer and Z is the set of all integers.

b)

k is a variable and Z represents a constant.

c)

k is a real number and Z is the set of rational numbers.

d)

k is a decimal and Z is the set of all whole numbers.

49.

If there is not limit in solutions for trig function, we can "find all solutions" by making a equation that includes by adding the solution by the period times a variable representing integers, right?

a)

No, that is not correct.

b)

Only specific solutions can be found.

c)

Yes, that is correct.

d)

The period does not affect the solutions.

50.

When stating the solutions, you should order them how?

a)

In ascending order

b)

By frequency of occurrence

c)

Random order

d)

In descending order

51.

When a degree is being multiplied in a trig function, is it true that you should multiply than the interval, find the angles that fit in it, and than divide it by what you multiplied by the interval?

a)

No, the method is only applicable to linear functions, not trigonometric ones.

b)

Yes, but you should add the multiplied value to the interval instead of dividing.

c)

Yes, this method is correct for adjusting angles in trigonometric functions.

d)

No, you should only multiply the angles directly without adjusting the interval.

52.

When having a trig function adding or subtracted to the degree, should we first find the angle and than subtract. Or subtract and than find the angle?

a)

Subtract the angle from the degree first.

b)

Find the angle first, then subtract.

c)

Find the angle and add instead of subtracting.

d)

Subtract first, then find the angle.

53.

When solving a trigonometric equation and there is degrees resembling a polynomial quadratic, can you replace the trig functions with a variable to find the solutions?

a)

Yes, you can replace trig functions with a variable.

b)

You should always keep the trig functions in their original form.

c)

Only if the equation is linear can you replace trig functions.

d)

No, you cannot replace trig functions with a variable.

54.

True or False: Most Trigonometric Equations have unique solutions

a)

False

b)

True

c)

All trigonometric equations have no solutions

d)

Most trigonometric equations have multiple solutions

55.

When writing a equation statement for tan, what can you do instead of adding 2pi for both solutions?

a)

Use x = arctan(y) + n*pi, where n is any integer.

b)

Use x = sin(y) + n*pi

c)

Set x = y + 90 degrees

d)

Use x = tan(y) + 2pi

56.

How can $\left(\sin\left(t\right)\right)^3$ also be written as in notation?

a)

sin^3(t)

b)

sin^2(t) * sin(t)

c)

(sin(t))^3

d)

sin(t)^3

57.

What is a Identity in math?

a)

An identity in math is an equation that holds true for all values of its variables.

b)

An identity is a type of mathematical function.

c)

An identity is a variable that changes value.

d)

An identity is a unique number in a set.

58.

What is the difference between conditional and identities in math?

a)

Identities are used only in geometry, while conditional statements apply to algebra.

b)

Conditional statements are equations that can change, while identities are fixed values.

c)

Conditional statements express a relationship between conditions, while identities are universally true equations.

d)

Conditional statements are always true, while identities depend on specific conditions.

59.

What is an example of a conditional statement in math vs idenity?

a)

Conditional statement: 'If x > 2, then x^2 > 4.'; Identity: 'x^2 - 1 = (x - 1)(x + 1).'.

b)

If x = 2, then x^2 = 4.

c)

If x < 0, then x^2 < 0.

d)

x^2 + 1 = (x + 1)(x - 1).

60.

When you have a trig function, you can ----- it!

a)

inverse

b)

evaluate

c)

simplify

d)

ignore

61.

What are the two quotient identities?

a)

tan(θ) = cos(θ) / sin(θ)

b)

cot(θ) = sin(θ) / cos(θ)

c)

tan(θ) = sin(θ) + cos(θ)

d)

tan(θ) = sin(θ) / cos(θ) and cot(θ) = cos(θ) / sin(θ)

62.

What do all six reciprocal identities have in common?

a)

They express the relationship between trigonometric functions and their reciprocals.

b)

They are only relevant in calculus.

c)

They are used to calculate angles in geometry.

d)

They only apply to sine and cosine functions.

63.

Why is it wrong to call sine the inverse of cosecant, and back and forth, instead of reciprocal?

a)

It is wrong to call sine the inverse of cosecant because they are reciprocals, not inverses.

b)

Sine and cosecant are the same function.

c)

Cosecant is the derivative of sine.

d)

Sine is the reciprocal of tangent.

64.

True or False: When establishing identities, its better to only focus on one side, the one with more complexity and free way, than mix or do the simple one.

a)

True

b)

False

c)

It doesn't matter which side to focus on

d)

Always start with the simpler side

65.

You can transform the identities of trig into the ones one needs

a)

Transformations are only possible with calculus.

b)

Trigonometric identities cannot be changed.

c)

Only advanced identities can be transformed.

d)

Trigonometric identities can be transformed using fundamental identities.

66.

Which Pythagorean Identity is equal to one? Use words

a)

Tangent squared plus cosine squared equals one.

b)

Sine squared minus cosine squared equals one.

c)

Sine squared plus tangent squared equals one.

d)

Sine squared plus cosine squared equals one.

67.

Which Pythagorean Identity is equal to $\sec^2x$ Use words

a)

sec^2x = cos^2x + sin^2x

b)

sec^2x = 1 - cos^2x

c)

sec^2x = tan^2x - 1

d)

sec^2x = 1 + tan^2x

68.

Which Pythagorean Identity is equal to $\csc^2\theta$ . Use words, not symbols.

a)

One minus sine squared of theta

b)

Two minus tangent squared of theta

c)

One plus sine squared of theta

d)

One plus cotangent squared of theta

69.

Addition/Subtraction Trig Identities are used to find exact values

a)

Addition/Subtraction Trig Identities are primarily for graphing functions.

b)

Addition/Subtraction Trig Identities are used for solving linear equations.

c)

Addition/Subtraction Trig Identities are only applicable to angles in degrees.

d)

Addition/Subtraction Trig Identities help in calculating exact values of trigonometric functions.

70.

True or False: Addition/Subtraction Trig Identies use special right triangles

a)

False

b)

True

c)

Only for specific angles

d)

Only for obtuse triangles

71.

If you have addition/subtraction trig identity that exceeds 90 degrees, you must use the reference angle of the new quadrant and the sign of the quadrant for the trig function

a)

Use the original angle without adjustment.

b)

Ignore the quadrant and use the angle directly.

c)

Always use a positive value for the trig function.

d)

Use the reference angle and the sign of the quadrant for the trig function.

72.

You can multiply a fraction in the denominator and numerator with any value if they are the same

a)

False

b)

Only for whole numbers

c)

Only if the value is greater than one

d)

True

73.

When doing Addition/Subtract Trig Identities, and you have csc, sec, and cot, you must the solving as a reciprocal

a)

Ignore csc, sec, and cot in calculations.

b)

Apply Pythagorean identities instead.

c)

Use reciprocal identities for csc, sec, and cot.

d)

Use direct multiplication for csc, sec, and cot.

74.

Is it true that trig functions are at its roots just a ratio

a)

Trig functions are only used in calculus.

b)

Trig functions are unrelated to geometry.

c)

Trig functions are solely based on angles.

d)

Yes, trig functions are fundamentally ratios.

75.

True or False: When using the half angle identity or addition and subtraction idenity, take a deep breath, and slowly find the ratios of the angles given. Remember sin(x), sin(y), cos(y), cos(x) are just equal to ratios

a)

True

b)

False

76.

Ratios or just angles inside trig functions

a)

Trigonometric ratios

b)

Algebraic ratios

c)

Geometric angles

d)

Trigonometric identities

77.

When given ratios, and told to use half angle or double angle functions, should the students draw out a triangle and than find the required ratios for cosine, sine, and tangent?

a)

No, students should use a calculator for all calculations.

b)

No, students should memorize the ratios instead.

c)

Yes, but only for sine and cosine, not tangent.

d)

Yes, students should draw a triangle to find the required ratios.

78.

Is it true that sine and cosine on their own cannot exceed 1 since the unit circle has a limit

a)

True

b)

Cosine can exceed 1

c)

Sine can exceed 1

d)

False

79.

True or False: Since and Cosine always have to add to one without being squared

a)

False

b)

Cosine is always greater than zero

c)

Sine and Cosine are always equal

d)

True

80.

Can sine and cosine both be negative 1 at the same time

a)

No, sine and cosine cannot both be -1 at the same time.

b)

Sine can be -1 while cosine is 0.

c)

Yes, sine and cosine can both be -1 at the same time.

d)

Both sine and cosine can be -1 at 90 degrees.

81.

When solving with trig identities, what tips can you give the student stuck in loops?

a)

Use only tangent functions

b)

Ignore the identities completely

c)

Focus on memorizing formulas

d)

Use sine and cosine, look for patterns, and simplify.

82.

True or False: When solving a trig function, and you square, how many solutions do you get?

a)

Two solutions

b)

One solution

83.

Is it true that you don't always have to keep on using trig identities to simplify or prove a trig function?

a)

Always required to use trig identities

b)

True

c)

Only in some cases

d)

False

84.

True or False: To rationalize a denominator with roots that are adding, you SHOULD NOT use congujate pairs to remove them

a)

Rationalizing is unnecessary for all roots

b)

False

c)

True

d)

You should always use conjugate pairs

85.

True or False: You have the freedom of solving trig functions in a larger way compared to other math concepts.

a)

True

b)

You have more freedom with trig functions than algebra.

c)

Trig functions are easier than other math concepts.

d)

False

86.

True or False: When solving for all soltuions of a trig functions, get values. Those aren't just the only ratios that gives angles, you must find all of them!

a)

True

b)

False

87.

What are the last words to have before an exam that is worrysome

a)

I am prepared.

b)

I hope for the best.

c)

I'm going to fail.

d)

I didn't study.

Unit 5 – Trig Functions - Radian - Vocab

Total questions: 87

Worksheet time: 47mins

Similar Resources on Wayground