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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