Reference no: EM131064773
1. Find the complete exact solution of sin x = -(√3/2).
2. Solve cos 2x - 3 sin x cos 2x = 0 for the principal value(s) to two decimal places.
3. Solve tan2x + tan x - 1 = 0.
4. Prove that tan2α-1 + cos2α = tan2α sin2α.
5. Prove that tanβ sinβ + cosβ = secβ.
6. Prove that (tanλcos2λ + sin2λ/sinλ) = cosλ + sinλ.
7. Prove that (1+tanθ/1-tanθ) = (sec2θ + 2tanθ/1-tan2θ).
8. Prove that (sin2ω-cos2ω/tanωsinω + cosωtanω) = cosω - cotω cosω
9. Find a counterexample to show that the equation sec α - cos α = sinα secα is not an identity.
10. Write tan(π/4 - β) as a function of β only.
11. Write cos(λ + π/3) as a function of λ only.
12. Write cos(-83o) as a function of a positive angle.
13. Write sin(125o) in terms of its co-function. Make sure your answer is a function of a positive angle.
14. Find the exact value of sin(195o).
15. Sketch a graph of y= sin(-2x), paying particular attention to the critical points.
16. If cot2θ = 5/12, with 0 ≤ 2θ ≤ π, find cosθ, sinθ, and tanθ.
17. Find the exact value of sin2α if cosα = 4/5 (α in Quadrant I).
18. Find the exact value of tan2β if sinβ = 5/13 (β in Quadrant II)
19. Solve sin2x + sinx = 0 for 0 ≤ x ≤ 2π.
20. Write 2sin37osin26o as a sum (or difference).
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: Prove that (sin2ω-cos2ω/tanωsinω + cosωtanω) = cosω - cotω cosω. Find a counterexample to show that the equation sec α - cos α = sinα secα is not an identity. Write tan(π/4 - β) as a function of β only
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