Download Advanced Algebra and Trigonometry – Section 5.3 Review

Advanced Algebra and Trigonometry – Section 5.3
Review
Objective: To review concepts from 5.3 – Evaluate trig functions of any angle, use the signs of trig functions,
and use reference angles to evaluate trig functions.
Do Now: Identify the quadrant in which the terminal side of θ in standard position lies given the
following:
1. sinθ is positive and cosθ is negative _____________________
2. secθ > 0 and tanθ < 0
________________________
3. cosθ < 0 and cscθ < 0 ________________________
____________________________________________________________________________________
Identify the quadrant in which the terminal side of θ in standard position lies given the following:
1. sinθ > 0 and cotθ < 0
________________________
2. secθ < 0 and sinθ < 0
________________________
3. cscθ > 0 and tanθ > 0
________________________
4. cosθ < 0 and tanθ < 0
________________________
5. sinθ > 0 and cosθ < 0
________________________
𝟒
6. Given 𝒕𝒂𝒏𝜽 = − 𝟑 and 𝒄𝒐𝒔𝜽 < 𝟎, draw a diagram and label it. Use your diagram to evaluate the
remaining trig ratios.
sinθ = _______________
cscθ = __________________
cosθ = _______________
secθ = __________________
tanθ = −
4
3
cotθ = __________________
𝟐
𝟓
7. Given 𝒔𝒊𝒏𝜽 = − and 𝟏𝟖𝟎𝒐 < 𝜽 < 𝟐𝟕𝟎𝒐 , draw a diagram and label it. Use your diagram to evaluate the
remaining trig ratios.
sinθ = −
2
cscθ = __________________
5
cosθ = _______________
secθ = __________________
tanθ = _______________
cotθ = __________________
8. For each of the following, find the reference angle θ’, use the quadrant in which θ lies to find the sign
and then find the exact value using reference angles.
(a) 𝒔𝒊𝒏
𝟓𝝅
𝟔
(b) 𝒄𝒐𝒔
(c) 𝒕𝒂𝒏𝟐𝟒𝟎𝒐
𝝅
𝟒
(e) 𝒄𝒐𝒔(− )
𝟒𝝅
𝟑
(d) 𝒔𝒊𝒏(−𝟐𝟐𝟓𝒐 )
(f) 𝒄𝒐𝒕
𝟓𝝅
𝟒
9. The point (7, –4) lies on the terminal side of angle θ in standard position. Draw the diagram for θ and
find the 6 trigonometric ratios of the angle.
sinθ = _______________
cscθ = __________________
cosθ = _______________
secθ = __________________
tanθ = _______________
cotθ = __________________
10. The point (–5, –12) lies on the terminal side of angle θ in standard position. Draw the diagram for θ
and find the 6 trigonometric ratios of the angle.
sinθ = _______________
cscθ = __________________
cosθ = _______________
secθ = __________________
tanθ = _______________
cotθ = __________________
11. Sketch the quadrantal angles. Then, evaluate the trigonometric function, or state that the
expression is undefined.
(a) 𝒔𝒊𝒏𝝅 = _____________
(b) 𝒄𝒔𝒄
𝟑𝝅
𝟐
= _____________
(c) 𝒕𝒂𝒏 𝟐 = _____________
𝝅
(d) 𝒔𝒆𝒄𝝅 = _____________
(e) 𝒄𝒐𝒕
𝟑𝝅
𝟐
= _____________
(f) 𝒄𝒐𝒔 𝟐 = _____________
𝝅