Trigonometric Ratios (Acute Angle) MCQs Quiz | Class 10
This quiz is designed for **Class X** students studying **Mathematics (Code 041)**, specifically **Unit V: Trigonometry**, focusing on **Trigonometric Ratios (Acute Angle)**. It covers fundamental concepts of sin, cos, tan, cot, sec, and cosec in a right-angled triangle. Test your knowledge by attempting all 10 multiple-choice questions, then submit to see your score and download a detailed PDF answer sheet for review.
Understanding Trigonometric Ratios for Acute Angles
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. In Class 10, we primarily focus on right-angled triangles and the ratios of their sides with respect to acute angles. These ratios are fundamental to solving problems involving heights, distances, and angles in various real-world scenarios.
Key Trigonometric Ratios
For a right-angled triangle, consider an acute angle ‘A’.
- Sine of angle A (sin A): Ratio of the side opposite to angle A to the hypotenuse.
- Cosine of angle A (cos A): Ratio of the side adjacent to angle A to the hypotenuse.
- Tangent of angle A (tan A): Ratio of the side opposite to angle A to the side adjacent to angle A.
A common mnemonic to remember these is SOH CAH TOA:
- SOH: Sin = Opposite / Hypotenuse
- CAH: Cos = Adjacent / Hypotenuse
- TOA: Tan = Opposite / Adjacent
Reciprocal Ratios
In addition to the primary ratios, there are three reciprocal ratios:
- Cosecant of angle A (cosec A): Reciprocal of sin A. (Hypotenuse / Opposite)
- Secant of angle A (sec A): Reciprocal of cos A. (Hypotenuse / Adjacent)
- Cotangent of angle A (cot A): Reciprocal of tan A. (Adjacent / Opposite)
These relationships are important:
- cosec A = 1 / sin A
- sec A = 1 / cos A
- cot A = 1 / tan A
Important Points to Remember
- The trigonometric ratios are dimensionless numbers.
- The values of sin A and cos A are always less than or equal to 1.
- The values of sec A and cosec A are always greater than or equal to 1.
- The values of tan A and cot A can be any positive real number for acute angles.
- The values of trigonometric ratios for specific angles (0, 30, 45, 60, 90 degrees) are fixed and should be memorized.
Practice Questions (without options)
- In a right triangle ABC, right-angled at B, if AB = 8 cm and BC = 15 cm, find sin A.
- If cos P = 3/5, find tan P.
- Given tan theta = 4/3, find the value of (sin theta + cos theta).
- If sin A = 1/2, calculate the value of (3 sin A – 4 sin cube A).
- In triangle PQR, right-angled at Q, PQ = 7 cm and PR = 25 cm. Determine the value of tan P – tan R.
