MCQ
Trigonometry MCQ - Practice Questions with Answers
Solve 60 Trigonometry questions for RAS/RPSC preparation.
Practice questions
Q1Angles p and q are complementary, and tan p + tan q = 26/5. Find (sin p − cos p)^2, correct to two decimal places.
As p and q are complementary, tan q = cot p. Thus tan p + cot p = 1/(sin p cos p) = 26/5, giving sin p cos p = 5/26. Now (sin p − cos p)^2 = 1 − 2 sin p cos p = 1 − 10/26 = 8/13 = 0.62 to two decimal places. Therefore, option A is correct.
Q2If sin² θ = 0.36, then cos² θ equals
The Pythagorean identity states sin² θ + cos² θ = 1. Rearrangement gives cos² θ = 1 − sin² θ = 1 − 0.36 = 0.64.
Q3The expansion sin 25° cos 65° + cos 25° sin 65° simplifies to which value?
The expression matches the sine-addition formula sin(A + B) with A = 25° and B = 65°. Therefore it equals sin 90° = 1.
Q4For an acute angle x, which expression is equal to the sine of its complement?
The cofunction identity gives sin(90° − x) = cos x. Hence the sine of the complement of x is cos x, so option A is correct.
Q5If y is acute and tan(90° − y) = 7/24, what is sin y, correct to two decimal places?
Since tan(90° − y) = cot y, cot y = 7/24 and therefore tan y = 24/7. The ratio 7:24 has hypotenuse 25 by the Pythagorean relation. Thus sin y = 24/25 = 0.96, so option A is correct.
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More questions
6A roof pitch is set at an acute angle θ where tan θ + cot θ = 4. The value of sin θ cos θ is:
7For an acute angle θ with cot θ = 8/15, evaluate (sec θ − tan θ)/(sec θ + tan θ).
8A navigation chart records that sin(θ + 15°) = cos(2θ − 45°) for an acute angle θ. What is θ?
9Survey bearings P and Q are complementary, so P + Q = 90°. Given sin P = 12/37, tan Q equals
10Given sin θ = 9/41 with θ acute, find (cosec θ + sec θ)/(cosec θ − sec θ).
11For v = 45 degrees, simplify (sin v + cos v)/(sin v cos v).
12Triangle PQR is right-angled at P. Which ratio is equal to sin Q?
13During a stock count, an auditor compares sin 30° with cos 60°. Sin 30° as a percentage of cos 60° equals:
14Let θ be acute with tan θ = 2/3. Find sec² θ + cosec² θ.
15A machine arm's pitch angle θ (acute) satisfies sec θ + tan θ = 5/2. The value of tan θ is: