Trigonometry

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Q1. If sin(θ) = 0.866, what is θ? (2022)

Solution:

sin(60°) = √3/2 ≈ 0.866, so θ = 60°.

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Q2. If cos(θ) = 0.5, what is the value of θ in degrees? (2017)

Solution:

cos(60°) = 0.5, so θ = 60°

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Q3. What is the value of tan(90°)? (2022)

Solution:

tan(90°) is undefined.

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Q4. If sin(θ) = 1, what is θ? (2023)

Solution:

sin(90°) = 1, so θ = 90°.

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Q5. If cos(θ) = 0.5, what is the value of θ? (2020)

Solution:

cos(60°) = 0.5, so θ = 60°.

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Q6. If sin(θ) = 1, what is the value of θ? (2023)

Solution:

sin(90°) = 1, so θ = 90°.

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Q7. If sin(θ) = 0.8, what is cos(θ)? (2022)

Solution:

Using sin²(θ) + cos²(θ) = 1, cos(θ) = √(1 - 0.8²) = √(0.36) = 0.6.

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Q8. If sin(θ) = 1/√2, what is cos(θ)? (2022)

Solution:

Using sin²(θ) + cos²(θ) = 1, cos(θ) = √(1 - (1/√2)²) = √(1/2) = √2/2

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Q9. If cos(θ) = 0.6, what is sin(θ) using Pythagorean identity? (2017)

Solution:

sin²(θ) + cos²(θ) = 1; sin²(θ) = 1 - 0.6² = 0.64; sin(θ) = √0.64 = 0.8.

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Q10. If sin(θ) = 1/√2, what is θ in degrees?

Solution:

sin(45°) = 1/√2, so θ = 45°