Radians and Review

​Reciprocal Trig Identities

Radians and Review | Reciprocal Identities

Multiple Choice

Secant is the reciprocal of what function?

• Cosecant

• Sine

• Cosine

• Tangent

Multiple Choice

Cotangent is the reciprocal of what function?

• Cosecant

• Sine

• Cosine

• Tangent

Multiple Choice

Cosecant is the reciprocal of what function?

• Secant

• Sine

• Cosine

• Tangent

Multiple Choice

Given the Cos(x) = -2/3, then the Sec(x) = ?

• -2/3

• -3/2

• 3/2

• 2/3

Multiple Choice

Given the Csc(x) = 1, then the Sin(x) = ?

• 1

• -1

• 0

• Undefined

Multiple Choice

Sec(π/3) = ?

• 1/2

• √(3)/2

• 2

• √3

Multiple Choice

Cot(5π/6) = ?

• √3

• -√3

• 2

• -√(3)/3

Multiple Choice

Use your calculator to evaluate: Csc(15⁰) = ?

• 1.537

• -1.316

• 3.864

• 1.035

​Exact Values of Trig Functions

​We can use the Unit Circle to evaluate the exact value of functions.​

Remember, the Unit Circle has a radius of 1 and ​points on the circle give the sine and cosine values of certain angles.

Multiple Choice

cos 90

• 0

• 1

• -1

• undefined

Multiple Choice

sin 150

• -1/2

• -√3/2

• 1/2

• √3/2

Multiple Choice

tan 225

• √2/2

• -√2/2

• 1

• -1

Multiple Choice

sec 300

• 2√3/3

• -2√3/3

• 2

• -2

Multiple Choice

What is the exact coordinates of  3π/4 on the unit circle?

• (−√2∕2, √2∕2)

• (−√2∕2, −√2∕2)

• (−√3∕2, −√2∕2)

• (√2∕2, −√2∕2)

Multiple Choice

What is the radius of a unit circle?

• 1

• 2

• 1/2

• 0

Multiple Choice

sin (π/2)

• √3/2

• √2/2

• 1/2

• 1

Multiple Choice

cos (π/4)

• √3/2

• √2/2

• 1/2

• 1

Multiple Choice

cos(5π/3)

• -√2/2

• -1/2

• 1/2

• √3/2

​Cofunctions with Radians

Remember, cofunctions are a relationship between trig functions that have complementary angles.

Remember, complementary means the angles sum to 90⁰​.

Multiple Select

Each trig function has a "cofunction" (Ex: sine and cosine are cofunctions).

How are cofunctions related to each other? (Check all that apply)

• Cofunctions of complementary angles are equal.

• Cofunctions are reciprocals of each other.

• Cofunctions are inverses of each other.

• Cofunctions are negatives of each other.

Multiple Choice

Which of these is false?

• $$\cos\left(\frac{\pi}{2}-\theta\right)=\sin\left(\theta\right)$$  

• $$\sin\left(\frac{\pi}{2}-\theta\right)=\cos\left(\theta\right)$$  

• $$\sec\left(\frac{\pi}{2}-\theta\right)=\cos\left(\theta\right)$$  

• $$\tan\left(\frac{\pi}{2}-\theta\right)=\cot\left(\theta\right)$$  

Multiple Select

Which is equal to $$\sin\ \frac{\pi}{3}$$  ? Pick all that apply.

• $$\sin\frac{\pi}{3}$$  

• $$\cos\frac{\pi}{3}$$  

• $$\cos\ \frac{\pi}{6}$$  

• $$\sin\ \frac{\pi}{6}$$  

Multiple Choice

If sin(2x+7)°=cos(4x−7)°, what is the value of x?

• 7

• 15

• 21

• 30

Multiple Choice

For the acute angles in a right triangle, csc(4x)° = sec(3x + 13)°. What is the number of degrees in the measure of the smaller angle?

• 1) 11°

• 2) 13°

• 3) 44°

• 4) 52°

Multiple Choice

Convert π radians to degrees.

• 90⁰

• 180⁰

• 360⁰

• 60⁰

Fill in the Blank

Convert $$\frac{π}{3}$$  from  radians to degrees

(type number only)

Multiple Choice

Convert  $$\frac{π}{4}$$   from radians to degrees

• 90⁰

• 45⁰

• 60⁰

• 30⁰

Multiple Choice

To convert from degrees to RADIANS

• multiply by

  $$\frac{π}{180°}$$

• multiply by $$\frac{180°}{π}$$

• multiply by $$\frac{π}{\sqrt{2}}$$

• multiply by $$\frac{π}{\sqrt{3}}$$

Multiple Choice

To convert from radians to DEGREES

• multiply by

  $$\frac{π}{180°}$$

• multiply by $$\frac{180°}{π}$$

• multiply by $$\frac{π}{\sqrt{2}}$$

• multiply by $$\frac{π}{\sqrt{3}}$$

Multiple Choice

Convert 150⁰ to radians

• $$\frac{5π}{6}$$

• $$\frac{3π}{4}$$

• $$\frac{7π}{6}$$

• $$\frac{2π}{3}$$

• $$\frac{15π}{8}$$

Multiple Choice

What is the degree of an angle with a radian measure of $$\frac{7}{4}\pi$$  

• $$310\degree$$  

• $$320\degree$$  

• $$315\degree$$  

• $$330\degree$$  

Multiple Choice

What is 360 degrees in radians? 

• 2π/3

• 5π/4

• 2π

• π

Multiple Choice

Convert to degrees: 11π/6

• 300°

• 315°

• 330°

• 350°