Trigonometric Functions

What you'll learn

Stop memorising blindly — understand angles as radians, meet sine and cosine on the unit circle, master the sign of each ratio in every quadrant, and see exactly where the key identities come from.

This chapter has

Trigonometric Functions — solved practice questions

8 Class 11 Mathematics questions with step-by-step solutions. Attempt each, then reveal the answer.

1. Q1easy

   The radian measure corresponding to 60 degrees is:

   • Api/6
   • Bpi/4
   • Cpi/3
   • Dpi/2
   Show answer & solution

   Correct answer: (C) pi/3

   Multiply degrees by pi/180: 60 x pi/180 = pi/3 radians.

2. Q2easy

   The degree measure corresponding to pi/6 radians is:

   • A30 degrees
   • B45 degrees
   • C60 degrees
   • D90 degrees
   Show answer & solution

   Correct answer: (A) 30 degrees

   Multiply radians by 180/pi: (pi/6) x (180/pi) = 30 degrees.

3. Q3easy

   The value of tan 45 degrees is:

   • A1
   • B0
   • Csquare root of 3
   • D1/square root of 3
   Show answer & solution

   Correct answer: (A) 1

   tan 45 degrees = sin 45 degrees / cos 45 degrees = 1.

4. Q4easy

   The value of sin 90 degrees is:

   • A0
   • B1/2
   • Csquare root of 3 / 2
   • D1
   Show answer & solution

   Correct answer: (D) 1

   sin 90 degrees = 1, which is its maximum value.

5. Q5medium

   The value of cos 120 degrees is:

   • A1/2
   • Bsquare root of 3 / 2
   • C-square root of 3 / 2
   • D-1/2
   Show answer & solution

   Correct answer: (D) -1/2

   cos 120 degrees = cos(180 - 60) degrees = -cos 60 degrees = -1/2, since cosine is negative in the second quadrant.

6. Q6medium

   In which quadrant is the sine of an angle positive but the cosine negative?

   • AFirst quadrant
   • BSecond quadrant
   • CThird quadrant
   • DFourth quadrant
   Show answer & solution

   Correct answer: (B) Second quadrant

   In the second quadrant sine is positive while cosine and tangent are negative.

7. Q7medium

   The value of sin 15 degrees is:

   • A(square root of 6 + square root of 2)/4
   • B(square root of 3 - 1)/2
   • C(square root of 6 - square root of 2)/4
   • D(square root of 2 - 1)/2
   Show answer & solution

   Correct answer: (C) (square root of 6 - square root of 2)/4

   sin 15 degrees = sin(45 - 30) degrees = sin45 cos30 - cos45 sin30 = (square root of 6 - square root of 2)/4.

8. Q8medium

   If sin x = 3/5 and x lies in the first quadrant, then cos x equals:

   • A3/4
   • B-4/5
   • C4/5
   • D5/4
   Show answer & solution

   Correct answer: (C) 4/5

   cos x = square root of (1 - sin squared x) = square root of (1 - 9/25) = square root of (16/25) = 4/5, positive in the first quadrant.

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