Trigonometry

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Q1. What is the value of cot(45°)?

Solution:

cot(45°) = 1/tan(45°) = 1/1 = 1

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Q2. If sin(θ) = 0.866, what is θ? (2022)

Solution:

sin(60°) = √3/2 ≈ 0.866, so θ = 60°.

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Q3. What is the value of tan(0°)? (2018)

Solution:

tan(0°) = 0

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Q4. What is the value of sec(45°)? (2019)

Solution:

sec(45°) = 1/cos(45°) = 1/(√2/2) = √2.

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Q5. What is the value of sin(45°)? (2016)

Solution:

sin(45°) = 1/√2

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Q6. If cos(θ) = 1/2, what is θ in degrees?

Solution:

cos(60°) = 1/2, so θ = 60°

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Q7. What is the value of cot(90°)? (2018)

Solution:

cot(90°) = 1/tan(90°) = 1/0 = undefined.

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Q8. 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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Q9. 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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Q10. If cos(θ) = 0.5, what is the value of θ? (2020)

Solution:

cos(60°) = 0.5, so θ = 60°.