Trigonometry

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Q1. If cos(θ) = 0.707, what is θ? (2020)

Solution:

cos(45°) = √2/2 ≈ 0.707, so θ = 45°.

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Q2. What is the value of sin(45°)? (2016)

Solution:

sin(45°) = 1/√2

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Q3. What is the value of cot(90°)? (2018)

Solution:

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

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Q4. 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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Q5. 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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Q6. What is the value of sec(45°)? (2019)

Solution:

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

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Q7. If cos(θ) = 1/2, what is θ in degrees?

Solution:

cos(60°) = 1/2, so θ = 60°

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Q8. If sin(θ) = 0.8, what is cos(θ) using Pythagorean identity? (2020)

Solution:

Using sin²(θ) + cos²(θ) = 1, cos²(θ) = 1 - 0.64 = 0.36, cos(θ) = 0.6

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Q9. If sin(θ) = 1, what is the value of θ in degrees? (2019)

Solution:

sin(90°) = 1, so θ = 90°.

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Q10. If tan(θ) = 1, what is the value of θ? (2020)

Solution:

tan(45°) = 1, so θ = 45°.