Maths · Sets and functions · chapter 3 of 14

Class 11 Maths Chapter 3: Trigonometric Functions Assertion-reason questions with answers

2 assertion-reason questions on Trigonometric Functions, each with its answer and the reason, written from the NCERT chapter. For school exams on the CBSE pattern and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter. Each question gives an Assertion (A) and a Reason (R); choose how they stand to each other.

Question 1
Assertion (A): cos 300° is positive. Reason (R): cos x is positive in the fourth quadrant.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

300° lies between 270° and 360°, in the fourth quadrant, where cos x (the x-coordinate on the unit circle) is positive: cos 300° = cos (360° − 60°) = 1/2. R is true and is the reason.

Question 2
Assertion (A): tan (π + x) = tan x for every x in the domain of tan. Reason (R): sin (2π + x) = sin x and cos (2π + x) = cos x for every real x.
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Answer: (b) Both A and R are true, but R is not the correct explanation of A.

A is true: tan (π + x) = sin (π + x)/cos (π + x) = (−sin x)/(−cos x) = tan x. R is true, but it is about an interval of 2π; A rests on sin (π + x) = −sin x and cos (π + x) = −cos x, which R does not give.

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