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

Assertion and Reason Questions for Class 10 Maths Chapter 8 Introduction to Trigonometry are available in this Maths article. Assertion and Reason Questions for Class 10 Maths Chapter 8 Introduction to Trigonometry are very useful to solve the problems easily. This article helps the students to know the key questions and answers about Introduction to Trigonometry. Trigonometry covers trigonometric ratios, values of angles, identities, and relationships between sine, cosine, tangent, secant, cosecant, and cotangent, which are important in exam practice. 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 of$\sin 30^\circ$is$\frac{1}{2}$.

Reason (R): In a$30^\circ-60^\circ-90^\circ$triangle, the side opposite to$30^\circ$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 of$\cos 0^\circ$is 1.

Reason (R): The side adjacent to angle$0^\circ$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 of$\tan 45^\circ$is 1.

Reason (R): In a$45^\circ-45^\circ-90^\circ$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 ratio$\sin \theta$is given by:

$\sin\theta=\frac{\text{Perpendicular}}{\text{Hypotenuse}}$

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 of$\sec 0^\circ$is 1.

Reason (R):$\sec \theta$ is the reciprocal of$\cos \theta$.

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.

$\sec 0^\circ=\frac{1}{\cos 0^\circ}=\frac{1}{1}=1$

Question 7:

Assertion (A): The value of $\cosec 90^\circ$ is 1.

Reason (R):$\cosec \theta$ is the reciprocal of$\sin \theta$.

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):$\tan 0^\circ = 0$

Reason (R):$\tan \theta = \frac{\sin \theta}{\cos \theta}$

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 of$\sin^2\theta+\cos^2\theta$ is always 1.

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

$\sin^2\theta+\cos^2\theta=1$

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):$\tan \theta$ is undefined for$\theta=90^\circ$.

Reason (R):$\cos 90^\circ = 0$.

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 of$\cot 45^\circ$is 1.

Reason (R):  $\cot \theta$is the reciprocal of$\tan \theta$.

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):$\sin 90^\circ = 1$

Reason (R): The perpendicular side becomes equal to the hypotenuse at$90^\circ$.

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

Question 13:

Assertion (A):$\sec \theta=\frac{1}{\cos \theta}$

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 of$\cos 60^\circ$is$\frac{1}{2}$.

Reason (R): In a $30^\circ-60^\circ-90^\circ$ triangle, the adjacent side to  $60^\circ$ 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):$\tan \theta = \frac{\sin \theta}{\cos \theta}$

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.

Download PDF - Assertion And Reason Questions For Class 10 Maths Chapter 8 Introduction To Trigonometry

Related Topics:

• Chapter 1: Real Numbers
• Chapter 2: Polynomials
• Chapter 3: Pair of Linear Equations in Two Variables
• Chapter 4: Quadratic Equations
• Chapter 5: Arithmetic Progression 
• Chapter 6: Triangles
• Chapter 7: Coordinate Geometry
• Chapter 9: Applications of Trigonometry
• Chapter 10: Circles
• Chapter 11: Areas Related to Circles
• Chapter 12: Surface Areas and Volumes
• Chapter 13: Statistics
• Chapter 14: Probability