Free Printable PreCalc Sem2 Exam: Trig identities/solve/polar

1.

$\tan\theta\ =$

a)

$\frac{\sin\theta}{\cos\theta}$

b)

$\frac{\cos\theta}{\sin\theta}$

c)

$\frac{1}{\cos\theta}$

d)

$\cot\theta$

2.

$\tan\theta\cos\theta$ can be written in a single trigonometric identity as:

a)

$\cos\theta$

b)

$\sin\theta$

c)

$\sec\theta$

d)

$\cot\theta$

3.

$\frac{1-\cos^2\theta}{\cos^2\theta}$ can be written in a single trigonometric identity as:

a)

$\cos^2\theta$

b)

$\sin^2\theta$

c)

$\sec^2\theta$

d)

$\tan^2\theta$

4.

Which fast food restaurant is famous for its golden arches?

a)

Wendy's

b)

McDonald's

c)

Burger King

d)

Subway

5.

$\cos\theta\ \csc\theta$ can be written in a single trigonometric identity as:

a)

$\cos\theta$

b)

$\sin\theta$

c)

$\sec\theta$

d)

$\cot\theta$

6.

Simplify

$\cot^2\theta\left(1+\tan^2\theta\right)$

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

7.

Who is the heroine in The Hunger Games?

a)

Peeta Mellark

b)

Primrose Everdeen

c)

Effie Trinket

d)

Katniss Everdeen

8.

Simplify

$\sin\theta\left(\csc\theta-\sin\theta\right)$

a)

$\sec\theta$

b)

$\cos^2\theta$

c)

$\sin^2\theta$

d)

$\frac{\sin^2\theta}{\cos^2\theta}$

9.

Simplify

$\tan x\csc x\cos x$

a)

$\frac{1}{\cos x}$

b)

1

c)

$\cot x$

d)

-1

10.

$\sin^{-1}\left(-\frac{1}{2}\right)$ = _____

a)

$\frac{\pi}{6}$

b)

$-\frac{\pi}{6}$

c)

$\frac{11\pi}{6}$

d)

$-\frac{5\pi}{6}$

11.

What movie features this song?

a)

b)

c)

d)

12.

Evaluate: $Sec^{-1}\left(-2\right)$

a)

$-\frac{\pi}{3}$

b)

$\frac{2\pi}{3}$

c)

$\frac{\pi}{3}$

d)

$-\frac{2\pi}{3}$

13.

Evaluate: $Tan^{-1}\left(\frac{\sqrt[]{3}}{3}\right)$

a)

$\frac{5\pi}{6}$

b)

$\frac{\pi}{3}$

c)

$\frac{\pi}{6}$

d)

$-\frac{\pi}{6}$

14.

Which one of Spongebob Squarepant's friends is fond of playing the clarinet?

a)

b)

c)

d)

15.

Solve for 0≤x≤2π

CHOOSE ALL THAT APPLY!!!!

4cos²x- 2 = 0

a)

π/3, 5π/3

b)

π/4, 7π/4

c)

3π/4, 5π/4

d)

π/6, 11π/6

16.

$Solve\ \ \cos x\ \tan x\ +\ \cos x\ =\ 0\ \ for\ 0\ \le\ x\ <\ 2\pi$

a)

$\frac{\pi}{4},\ \frac{\pi}{2},\ \frac{5\pi}{4},\ \frac{3\pi}{2}$

b)

$0,\ \frac{3\pi}{4},\ \pi,\ \frac{7\pi}{4}$

c)

$\frac{\pi}{2},\ \frac{3\pi}{4},\ \frac{3\pi}{2},\ \frac{7\pi}{4}$

d)

$0,\ \frac{\pi}{4},\ \pi,\ \frac{5\pi}{4}$

17.

Which movie features this song?

a)

b)

c)

d)

18.

Solve equation for $0\le\theta<2\pi$ .
$0=2\sin^2\theta\ +\ \sqrt{3}\sin\theta$

a)

$\theta=0,\frac{2\pi}{3},\pi,\frac{5\pi}{3}$

b)

$\theta=\frac{\pi}{2},\frac{7\pi}{6},\frac{3\pi}{2},\frac{11\pi}{6}$

c)

$\theta=0,\pi,\frac{4\pi}{3},\frac{5\pi}{3}$

d)

$\theta=0,\pi,\frac{5\pi}{3}$

19.

Using the formulas on the notes, change the point $\left(2,\ \frac{\pi}{6}\right)$ into rectangular (x, y) form.

a)

$\left(\frac{\sqrt{3}}{2},\ 1\right)$

b)

$\left(\sqrt{3},\ 1\right)$

c)

$\left(2,\ \frac{\sqrt{3}}{2}\right)$

d)

$\left(1,\ \sqrt{3}\right)$

20.

Which house at Hogwarts does Harry Potter belong to?

a)

b)

c)

d)

21.

Which point(s) represents the graphed point in this polar coordinate plane? CHOOSE ALL THAT APPLY!

a)

$\left(4,\ -\frac{3\pi}{4}\right)$

b)

$\left(-4,\ \frac{\pi}{4}\right)$

c)

$\left(-4,\ \frac{3\pi}{4}\right)$

d)

$\left(4,\ -\frac{\pi}{4}\right)$

22.

Which place is called “the happiest place in the world?”

a)

b)

c)

d)

23.

Find the rectangular coordinates of each polar point. (4, 3π/2)

a)

(-4,-4)

b)

(-4,0)

c)

(0,-4)

d)

(0,-1)

24.

Which movie franchise is famous for this theme song?

a)

b)

c)

d)

25.

Convert from rectangular to polar coordinates. (-4, 4)

a)

(4√2, π/4)

b)

(4√2, 3π/4)

c)

(4√2, -π/4)

d)

(-4√2, -7π/4)

26.

Find polar coordinates for the point:
(√3 , 1)

a)

(2, π/6)

b)

(-2, -π/6)

c)

(1,0)

d)

(4π,-2)

27.

Which Steven Spielberg character appears in the Imperial Senate in Phantom Menace?

a)

Indiana Jones

b)

The shark from Jaws

c)

E.T.

d)

A velociraptor

28.

Express the point in polar form in rectangular form.
4 ( cos π /3 + i sin π /3)

a)

2 + 2√3 i

b)

2 + √3 i

c)

2 - 2√3 i

d)

-2 + 2√3 i

29.

Convert 5√3 - 5i to Polar (cis) Form.

a)

√40 cis(11π/6)

b)

10 cis(π/6)

c)

10 cis(11π/6)

d)

√40 cis(-π/6)

30.

Good _____ are good _____. CHOOSE ALL THAT APPLY!

a)

Foilers, factorers.

b)

Factorers, foilers

c)

cheaters, math students

d)

students, photomathers

31.

Convert (-√2 - √2i) to Polar (cis) Form.

a)

4 cis(π/4)

b)

2 cis(π/4)

c)

4 cis(5π/4)

d)

2 cis(5π/4)

32.

Match the correct polar equation with the following graph:

a)

r=1+cosθ

b)

rsinθ=2

c)

r=1-2sinθ

d)

r=2

33.

A student who copies HW keys or their friends work or uses photomath is .......

a)

A common core copying communist bum whose building a house of cards that WILL inevitably come crashing down!

b)

A smart student

c)

forming a strong, positive pattern of behavior that will lead to success in life

d)

forming a strong mathematical base that will lead to math success later in life.

34.

Which of the following could be the equation for...

a)

r = 6 + 6 sin θ

b)

r = 12 sin θ

c)

r = 6 - 6 sin θ

d)

r = 6 + 6 cos θ

35.

When someone drops something, you should....

a)

Yell "FUMBLE" and pounce on that object like it was a football.

b)

Kick it further away from the individual as they try to pick it up.

c)

Yell "AHH HAA" like Nelson on the Simpsons

36.

Which of these is an equation for this dimpled limaçon?

a)

r = 3 + 2 cosθ

b)

r = 2 + 3 cosθ

c)

r = 2 + 2cosθ

d)

r = 2 - 3cosθ

37.

This word is defined as a person who falsely claims to have a special knowledge or skill; a fraud. Synonyms to this word include quack, sham, fraud, fake, impostor, pretender, masquerader, hoodwinker, hoaxer, cheat, deceiver, double-dealer, double-crosser, trickster, cheater, swindler, fraudster, racketeer.

a)

charlatan

b)

A good student

c)

Honorable

d)

Scholarly

38.

This particular equation generates what graph

a)

b)

c)

d)

39.

People with a strong _____ perceive that they themselves have control over their own actions as opposed to events in life occurring solely because of external forces. They perceive themselves as having a great deal of personal control over their behavior and are therefore more likely to take responsibility for the way they behave. For example, I did well on the exams because I studied extremely hard.

a)

Internal locus of control

b)

External locus of control

c)

Ability to cheat

d)

Ability to blame others for their shortcomings

40.

Which of the following could be the equation for...

a)

r = sin 4θ

b)

r = 6 sin 2θ

c)

r = 6 cos 2θ

d)

r = cos 4θ

41.

If a student approached Mr. Samuilis' desk asking how to do a question on a test, he would say..

a)

"YOU'RE GONE! This is your time to tell me how to do this. If I answered that question, then I'd have to put my name on this test because now I'm answering the questions!"

b)

Here, let me answer this question and three more for you since you did not prepare properly

42.

What is the equation?

a)

r = 4

b)

r = 8

c)

r = 4sin(Θ)

d)

r = 8sin(Θ)

43.

A person comes up to Mr. Samuilis' desk or emails "can I have extra credit because I don't like my grade", Mr. Samuilis will say.......

a)

Sure, just tell me the grade you want!

b)

Your grade is a compilation of you're effort and ability to acheive right answers from January up until today. Your only chance to improve now is these last little quizzes and the final. That's how real classes work in college!

PreCalc Sem2 Exam: Trig identities/solve/polar

Total questions: 43

Worksheet time: 30mins

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