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Q1. In a right triangle, if the opposite side is 3 and the hypotenuse is 5, what is sin(θ)?
Solution:
sin(θ) = opposite/hypotenuse = 3/5
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Q2. Which of the following is the correct identity for sin²(θ) + cos²(θ)?
Solution:
sin²(θ) + cos²(θ) = 1
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Q3. If sin(θ) = 0.6, what is θ in degrees (to the nearest degree)?
Solution:
θ = arcsin(0.6) ≈ 36.87°, rounded to 37°
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Q4. If cos(θ) = 0.8, what is the value of θ in degrees (to the nearest degree)?
Solution:
θ = arccos(0.8) ≈ 36.87°, rounded to 37°
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Q5. If sin(θ) = 0.8, what is the value of θ in degrees?
Solution:
θ = sin⁻¹(0.8) ≈ 53.13°
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Q6. If a tree casts a shadow of 10 meters and the angle of elevation to the top of the tree is 45 degrees, what is the height of the tree?
Solution:
height = shadow * tan(45°) = 10 * 1 = 10 meters
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Q7. If sin(θ) = 0.6, what is the value of cos(θ) using the Pythagorean identity?
Solution:
cos(θ) = √(1 - sin²(θ)) = √(1 - 0.36) = √0.64 = 0.8
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