8.3 Unit Circle

Question 1

A 30-60-90 triangle with hypotenuse length 1 has leg lengths ? and ?

Answer 1

√3/2 and 1/2

Question 2

A 45-45-90 triangle with hypotenuse length 1 has a leg length of ?

Answer 2

√2/2

Question 3

List the positive trig ratios for each quadrant.

Answer 3

(from quadrant I to IV): all, sin, tan, cos

same for the reciprocals

Question 4

List the trig ratios that correspond to x, y, and slope.

Answer 4

cos θ = x
sin θ = y
tan θ = slope or y/x

Question 5

quadrantal angle definition

Answer 5

angle in standard position, terminal side lies on x-axis or y-axis

Question 6

reference angle definition

Answer 6

acute positive angle θ’ between the terminal side of θ and the x-axis

Question 7

how to use reference angle to evaluate function

Answer 7

1. find which quadrant the angle ends in
2. find if that trig ratio is positive/negative in that quadrant to determine whether answer will be positive or negative
3. find reference angle (special triangle angle)
4. refer to special triangle trig ratios