Solving Trigonometric Equations

Solve for Principal Values:

Sum and Differences Identities and Solving Trig Equations

Multiple Choice

1) 2sin²x - sinx - 1 = 0

• x = 3π/2, x = π/2

• x = π/4, x = π/2

• x = 5π/4, x= 3π/2

• x = π/2, x = π/6

Multiple Choice

2) 3cosx - 2 = 0

^{Solve x over the interval [0,2π]}

• 1.047
• 0.841
• 2.094
• 3.142

Multiple Choice

3)4tan²x - 1 = 0

^{Solve x over the interval [0,2π]}

• x = π/6, 5π/6
• x = 3π/4, 7π/4
• x = π/3, 2π/3
• x = π/2, 3π/2

Multiple Choice

4) 2sin²x = 5sinx + 3

• x = 7π/6, 5π/6

• x = 7π/6, 11π/6

• x = 5π/6, 11π/6

• x = 5π/6, π/6

Multiple Choice

5) 2sin²x - 3sinx + 1 = 0

• x = π/3, 4π/3

• x = π/4, 3π/4

• x = π/2, 7π/6

• x = π/6, π/2

Find exact values:

Multiple Choice

^{Use the boundaries 0 < x < π/2, 0 < y < π/2}

6) Find the exact value of sin (x+y) if sin x= 3/5 and sin y= 7/8

• 3√15/40 + 21/40

• √34/40 + 3√113/40

Multiple Choice

7) Find cos 180

• 0

• -1

• 1

Multiple Choice

8) tan (x+y) if csc x= 5/3 and cos y= 8/17

• 100/-13

• 85/96

• 72/85

• -13/96

Double Identities:

Multiple Choice

cos2θ/cosθ - sinθ = cosθ + sinθ

9) What is the last step before the answer?

• cos²θ/sinθ + sin²θ/cosθ

• cosθ/cos²θ + sinθ/cos²θ

• cos²θ/cosθ + sin²θ/sinθ

• sinθ/cos²θ + cosθ/sin²θ

Multiple Choice

10) Find sin2θ, cos2θ, and tan2θ if cotθ = 13/7

^{180 < θ < 270}

• sin2θ = -13/-40, cos2θ = -218/169, tan2θ = 13/218

• sin2θ = -13/7, cos2θ = -49/169, tan2θ = 13/49
• sin2θ = 147/218, cos2θ = -40/218, tan2θ = 147/-40

• sin2θ = -13/7, cos2θ = -13/169, tan2θ = 13/13

Verify (focus only on left side of equation):

Multiple Choice

sin (270 + A) = -cos A

11) What is the last step before verifying (=)?

• -1(cos A) + 0(sin A)

• 1(cos A) + 0(sin A)

• 0(cos A) + 1(sinA)

• 0(cos A) + -1(sin A)

Multiple Select

tan (θ + 2π) = tan θ

12) What is the first and second step? (Choose 2 answers)

• sin(θ+2π) /cos(θ+2π)

• cos(θ+2π)

  /sin(θ+2π)

• cosθcos2π - sinθsin2π /sinθcos2π + cosθsin2π

• sinθcos2π + cosθsin2π / cosθcos2π - sinθsin2π

Multiple Select

sec x - cos x = sinxtanx

13) What are one of the Identities used on the problem? (choose 2)

• secx = 1/cosx

• cotx = cosx/sinx

• sin²x = 1 - cos²x

• cos²x = 1 - sin²x