Assertion and Reason Questions for Class 10 Maths Chapter 8 Introduction to Trigonometry PDF

Assertion and Reason Questions for Class 10 Maths Chapter 7 Coordinate Geometry are available in this Maths article. Assertion and Reason Questions for Class 10 Maths Chapter 7 Coordinate Geometry are very useful to solve the problems easily. This article helps the students to know the key questions and answers about Coordinate Geometry. Coordinate geometry helps us find distances, midpoints, and areas using points on a graph, which we use in everyday calculations. Our subject experts have provided detailed solutions for these problems based on the CBSE syllabus and the NCERT textbook. This material helps students revise the chapter easily and perform well in the final examination. A free downloadable PDF is also available for easy practice and revision. 

Important Assertion And Reason Questions On Introduction To Trigonometry

Directions: In the following questions a statement of assertion (A) is followed by a statement of reason(R). Mark the correct choice as:

Choose the correct option for the following questions:

• (A). Both Assertion (A) and Reason (R) are true, and Reason is the correct explanation of Assertion.

• (B). Both Assertion (A) and Reason (R) are true, but Reason is not the correct explanation of Assertion.

• (C). Assertion (A) is true, but Reason (R) is false.

• (D). Assertion (A) is false, but Reason (R) is true.

Question 1:

Assertion (A): Trigonometric ratios are defined with respect to the angles of a right triangle.

Reason (R): A right triangle contains one angle equal to (90^\circ).

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (B). Both A and R are true, but R is not the correct explanation of A.

Question 2:

Assertion (A): The value ofsin⁡30∘is12.

Reason (R): In a30∘−60∘−90∘triangle, the side opposite to30∘is half the hypotenuse.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 3:

Assertion (A): The value ofcos⁡0∘is 1.

Reason (R): The side adjacent to angle0∘is equal to the hypotenuse.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 4:

Assertion (A): The value oftan⁡45∘is 1.

Reason (R): In a45∘−45∘−90∘triangle, the opposite side and adjacent side are equal.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 5:

Assertion (A):

The trigonometric ratiosin⁡θis given by:

sin⁡θ=PerpendicularHypotenuse

Reason (R): The hypotenuse is the longest side of a right triangle.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (B). Both A and R are true, but R is not the correct explanation of A.

Question 6:

Assertion (A): The value ofsec⁡0∘is 1.

Reason (R):sec⁡θ is the reciprocal ofcos⁡θ.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

sec⁡0∘=1cos⁡0∘=11=1

Question 7:

Assertion (A): The value of \cosec90∘ is 1.

Reason (R):\cosecθ is the reciprocal ofsin⁡θ.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 8:

Assertion (A):tan⁡0∘=0

Reason (R):tan⁡θ=sin⁡θcos⁡θ

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 9:

Assertion (A): The value ofsin2⁡θ+cos2⁡θ is always 1.

Reason (R): This is a fundamental trigonometric identity.

sin2⁡θ+cos2⁡θ=1

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 10:

Assertion (A):tan⁡θ is undefined forθ=90∘.

Reason (R):cos⁡90∘=0.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 11:

Assertion (A): The value ofcot⁡45∘is 1.

Reason (R):  cot⁡θis the reciprocal oftan⁡θ.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 12:

Assertion (A):sin⁡90∘=1

Reason (R): The perpendicular side becomes equal to the hypotenuse at90∘.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 13:

Assertion (A):sec⁡θ=1cos⁡θ

Reason (R): Secant is the reciprocal ratio of cosine.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 14:

Assertion (A): The value ofcos⁡60∘is12.

Reason (R): In a 30∘−60∘−90∘ triangle, the adjacent side to  60∘ is half the hypotenuse.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 15:

Assertion (A):tan⁡θ=sin⁡θcos⁡θ

Reason (R): Division of the sine ratio by the cosine ratio gives the tangent ratio.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

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