Trigonometry
Ten quantitative aptitude questions, each marked as you answer.
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What is the value of 3 cot² 60° − 3 cosec 30°?
Answer and working
Answer C
cot² 60° = 1⁄3 and cosec 30° = 2. So 3 × 1⁄3 − 3 × 2 = −5.
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What is the value of 2 cos 60° + 2 tan 45°?
Answer and working
Answer B
cos 60° = 1⁄2 and tan 45° = 1. So 2 × 1⁄2 + 2 × 1 = 3.
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What is the value of tan 45° − 2 sin 0°?
Answer and working
Answer D
tan 45° = 1 and sin 0° = 0. So 1 − 2 × 0 = 1.
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What is the value of cot 45° − 2 cot² 60°?
Answer and working
Answer A
cot 45° = 1 and cot² 60° = 1⁄3. So 1 − 2 × 1⁄3 = 1⁄3.
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If tan θ = 5⁄12 and θ is acute, what is cos θ?
Answer and working
Answer B
Draw a right triangle with sides 5, 12 and hypotenuse 13 (5² + 12² = 13²). Then cos θ = 12⁄13.
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What is the value of 3 cos 60° − 2 sin 0°?
Answer and working
Answer C
cos 60° = 1⁄2 and sin 0° = 0. So 3 × 1⁄2 − 2 × 0 = 3⁄2.
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If cos θ = 12⁄13 and θ is acute, what is cosec θ?
Answer and working
Answer D
Draw a right triangle with sides 5, 12 and hypotenuse 13 (5² + 12² = 13²). Then cosec θ = 13⁄5.
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What is the value of sin 30° − 3 cosec 30°?
Answer and working
Answer B
sin 30° = 1⁄2 and cosec 30° = 2. So 1⁄2 − 3 × 2 = −11⁄2.
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From a point on the ground 100 m from the foot of a tower, the angle of elevation of its top is 45°. How tall is the tower?
Answer and working
Answer D
Height = 100 × tan 45° = 100 × 1 = 100 m.
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If tan θ = 3⁄4 and θ is acute, what is sec θ?
Answer and working
Answer D
Draw a right triangle with sides 3, 4 and hypotenuse 5 (3² + 4² = 5²). Then sec θ = 5⁄4.
More quantitative aptitude: Percentages, Profit, loss and discount, Simple interest, Compound interest, Ratio and proportion, Averages.