Unit 2 Test 2

Quadrants

100

What trigonometric functions are positive in Quadrant I? 

All of them! Sin, Cos, Tan, Csc, Sec, Cot

200

What quadrant(s) is sin positive? 

Quadrants I & II

300

What quadrant(s) is tan positive? 

Quadrant I & III

400

What are ALL the trig functions that are negative in Quadrant IV?

Sin, Csc, Tan, Cot

500

If CosA= -3/4 and Cot > 0, what quadrant is the terminal side of angle A in? 

Quadrant III

Identities

100

Which two angles would you use to find the cos(75^o)?

45^o and 30^o

200

Find sin(75^o)= 

sin(45^o)*cos(30^o)+cos(45^o)*sin(30^o)= 

[sqrt(6)+sqrt(2)]  /  4

300

Find cos(x/2) 

cos(x/2) = +/- sqrt[(1+cosx)/2]

400

Rewrite the cos(2A) formula in terms of sinA (or sin²A) only

Cos(2A) = cos²A-sin²A = (1-sin²A) - sin²A = 1 - 2sin²A

500

Find sin(2A) if tan(A) = 1/2and sin(A) > 0

4/5

Laws

100

What information do you need to use the Law of Sines?

Multiple answers: 

AAS, SSA, or can say a side and angle pair

200

Given ∠A=30^o, ∠B=45^o, and side a = 4 find ∠C

C = 105^o

300

When is the Law of Cosines necessary over the Law of Sines?

When you have 2 sides and an interior angle or 3 sides and no angles. 

400

Rewrite the Law of Cosines to solve for A = 

A = cos^-1[(b²+c² - a²)/2bc]

500

In a triangle ABC, a=7, A=30^o∘, and B=45^o, find side b (round to tenths place)

b = 9.9

Special Angles

100

What is the reference angle for 150^o?

30^o

200

What is a coterminal angle for 450^o?

Many answers! Includes: 90, -270, 810, etc. 

Must add or subtract multiples of 360⁰

300

How do you find the reference angle for an angle that has a terminal side in the third Quadrant (ex. 240^o)?

Subtract 180^o from the given angle

400

What is the reference angle for 330^o?

30^o

500

What angles in Q2,3, and 4 have a reference angles equal to 40^o?

QII: 140^o

QIII: 220^o

QIV: 320^o