Trig Part 2 Final Exam Review Key

Trig Part 2 - More Unit Circle, Graphs, Identities, and Formulas Convert from degrees to radians 45° = π/4 -60° = -π/3 Convert from radians to degrees 3π/4 = 135° -11π/6 = -330° Complete the following: Angle Sin Cos Tan Csc Sec Cot 90° 1 0 undef. 1 undef. 0 180° 0 -1 0 undef. -1 undef. 270° -1 0 undef. -1 undef. 0 360° 0 1 0 undef. 1 undef. Give the exact value for each problem: 0 ≤ θ ≤ 360° sin 60° = √3/2 cos 120° = -1/2 sec θ = undefined, where θ = 90°, 270° (Quadrantal Angles) sin θ = -√3/2, 240°, 300° (Quadrants III & IV) Draw a triangle for each problem and find the exact value - no decimals! Find sin θ, if cot θ = 3/4 and 0° < θ < 90° sin θ = 4/5 right triangle with sides 3, 4, and 5 Find sec θ, if tan θ = -3/2 and 180° < θ < 270° sec θ = -√13/2 right triangle with sides 3, 2, and √13 Find cos θ, if tan θ = -15/8 and the angle is in the third quadrant. cos θ = -8/17 right triangle with sides 8, 15, and 17 Find cot θ, if csc θ = 5 and 270° < θ < 360° cot θ = -2√6 right triangle with sides 1, 2√6, and 5 Tell which quadrant each angle lies in (I, II, III, or IV). cos θ is positive and tan θ is negative. Quadrant IV csc θ is positive and tan θ is negative. Quadrant II tan θ is positive and sec θ is negative. Quadrant III TRIG. PART 2 - More Unit Circle, Graphs, Identities, and Formulas Give the amplitude, period and phase shifts (up/down/left/right) of each graph. You do not need to graph these. 17. y = 2 sin(θ - 180°) + 1 Amplitude: 2 Period: 360° Phase shift: 180° right Vertical shift: 1 up 18. y = -3 cos θ - 4 Amplitude: 3 Period: 360° Reflection: Yes Vertical shift: 4 down 19. y = (1/2) sin(θ + 90°) Amplitude: 1/2 Period: 360° Phase shift: 90° left Reflection: Yes Directions: Answer the following questions for the sine and cosine graphs. 20. Which equation is shown on the graph at the right? C. y = 2cos θ (Parent function for cosine in blue) 21. Which equation is shown on the graph at the right? D. y = sin θ - 1 (Parent function for sine in blue) 22. What is the vertical shift shown on the graph at the right? Down 1 unit 23. Which equation is shown on the graph at the right? B. y = cos θ + 2 (Parent function for cosine in blue) 24. What is the amplitude shown on the graph at the right? Amplitude of 2 25. Which equation is shown on the graph at the right? C. y = 2 sin θ (Parent function for sine in blue) 26. What is the amplitude shown on the graph at the right? Amplitude of 2 TRIG. PART 2 Use your formula sheet to remind yourself of the trig identities. Simplify. Show all work. 27. (sin θ sec θ)/(cot θ tan θ) = (sin θ / cos θ) / (cos θ / sin θ) = (sin²θ) / (cos²θ) = tan²θ 28. (sin²θ - cos²θ)/(sin θ cos θ) = (sin²θ - (1 - sin²θ)) / (sin θ cos θ) = (2sin²θ - 1) / (sin θ cos θ) Use your formula sheet to remind yourself of the sum and difference formulas. Use the sum and difference formulas to find the EXACT value of each trig. function. Rationalize when necessary! 29. cos 255° cos(30° + 225°) cos α cos β - sin α sin β cos 30° cos 225° - sin 30° sin 225° (√3/2)(-√2/2) - (1/2)(-√2/2) (-√6 - √2) / 4 30. sin 285° sin(45° + 240°) sin α cos β + cos α sin β sin 45° cos 240° + cos 45° sin 240° (√2/2)(-1/2) + (√2/2)(-√3/2) (-√2 - √6) / 4 31. tan 15° OMIT 32. cos 195° cos(60° + 135°) cos α cos β - sin α sin β cos 60° cos 135° - sin 60° sin 135° (1/2)(-√2/2) - (√3/2)(-√2/2) (-√2 - √6) / 4 33. sin 105° sin(45° + 60°) sin α cos β + cos α sin β sin 45° cos 60° + cos 45° sin 60° (√2/2)(1/2) + (√2/2)(√3/2) (√2 + √6) / 4 34. tan 285° OMIT