## Trigonometry Challenge: Get Your Angle On!

Instructions: Choose the best answer for each question.

1. If sin θ = 3/5 and θ is in Quadrant I, what is the value of cos θ?
  A. 4/5
  B. -4/5
  C. 3/4
  D. -3/4

Answer: A

2. What is the exact value of tan (150°)?
  A. √3
  B. -√3
  C. 1/√3
  D. -1/√3

Answer: D
The correct answer is D. -1/√3. Here's how to find it:
👉150° is in the second quadrant. Its reference angle is 30° (180° - 150°). Tangent is negative in the second quadrant.vtan(30°) = 1/√3. Since tan(150°) is negative and has the same magnitude as tan(30°),
  tan(150°) = -1/√3

3. If cos θ = -1/2 and θ is in Quadrant II, what is the value of sin θ?
  A. √3/2
  B. -√3/2
  C. 1/2
  D. -1/2

Answer: A
Explanation: Use the Pythagorean identity and the fact that sin θ is positive in Quadrant II.

4. Simplify the expression: (sin²x + cos²x) / tan x
  A. cos x
  B. sin x
  C. cot x
  D. tan x

Answer: C
Explanation: Use the Pythagorean identity and the definition of Cotangent.

5. Solve the equation: 2sin²x - sin x - 1 = 0 for 0 ≤ x ≤ 2π.
  A. π/2, 3π/2
  B. π/6, 5π/6
  C. π/3, 2π/3
  D. π/6, 5π/6, 3π/2

Answer: D
Explanation: Factor the quadratic equation and solve for sin x. Find the angles where sin x satisfies the solutions.

6. Simplify the expression: (1 + cot²θ) / (1 + tan²θ)
  A. cot²θ
  B. tan²θ
  C. 1
  D. sin²θ

Answer: A
Explanation: Use the Pythagorean identities for cot²θ and tan²θ.

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