Mathematics Exam Questions and Answers for Class 10 on “Trigonometric Ratios – 2”.
1. Trigonometric ratios are only applicable to which kind of triangles?
a) Right-angled triangles
b) Any type of triangles
c) Acute angled triangles
d) Obtuse angled triangles
Answer: a
Clarification: Trigonometric ratios are only applicable to right-angled triangles whose angle is 90° between two sides of a triangle.
2. Trigonometric ratios are ______
a) sine, cosine and cotangent
b) sine, tangent, cotangent and secant
c) sine, cosine, tangent, cotangent, secant and cosecant
d) tangent, cotangent and secant
Answer: c
Clarification: Trigonometric ratios are generally defined as the ratios of any two sides of a right-angled triangle and it gives the relation between sides of a right-angled triangle to its appropriate angle. Sine, cosine, tangent, cotangent, secant and cosecant are six trigonometric ratios used in trigonometry.
3. What is the inverse of cosecant?
a) Cosine
b) Secant
c) Sine
d) Tangent
Answer: c
Clarification: The inverse of cosecant is sine.
Cosec θ = (frac {1}{Sin theta })
4. (frac {Sin theta }{Cos theta}) equals to ______
a) tan θ
b) cot θ
c) cosec θ
d) sec θ
Answer: a
Clarification: Sin θ = (frac {Length , of , opposite , side , of , the , triangle}{Length , of , hypotenuse , of , the , triangle})
Cos θ = (frac {Length , of , adjacent , side , of , the , triangle}{Length , of , hypotenuse , of , the , triangle})
(frac {Sin theta }{Cos theta} = frac {Length , of , opposite , side , of , the , triangle}{Length , of , adjacent , of , the , triangle})
= Tan θ
5. Who is the ‘Father of Trigonometry’?
a) Hipparchus
b) Euclid
c) Aristotle
d) Archimedes
Answer: a
Clarification: Hipparchus was a Greek mathematician and is considered as the ‘Father of Trigonometry’. Hipparchus not only contributed to mathematics but also to astronomy.
6. The product of sin θ and Cosec θ is 1.
a) True
b) False
Answer: a
Clarification: The inverse of cosecant is sine.
Sin θ = (frac {1}{Cosec theta })
Sin θ.Cosec θ = 1
7. What is the cotangent of an angle θ if the side adjacent to θ is 8 units and the side opposite to θ is 3 units?
a) (frac {3}{8})
b) (frac {8}{3})
c) (frac {4}{3})
d) (frac {3}{4})
Answer: b
Clarification: Cotangent θ = (frac {Length , of , adjacent , side , of , the , triangle}{Length , of , opposite , of , the , triangle})
= (frac {8}{3})
8. Choose the correct reciprocal ratios.
a) Tan θ, Sec θ
b) Cosec θ, Sec θ
c) Sec θ, Sin θ
d) Tan θ, Cot θ
Answer: d
Clarification: Tan θ, Cot θ are the reciprocal ratios because they are inverse to each other.
Tanθ = (frac {1}{Cot theta })
9. The basic trigonometric ratios are _____
a) sine
b) tangent
c) sine, cosine and tangent
d) cosine
Answer: c
Clarification: The basic trigonometric ratios are sine, cosine and tangent and the other three trigonometric ratios secant, cosecant, cotangent are derived from these basic trigonometric ratios.
10. (frac {Length , of , hypotenuse}{Length , of , opposite , to , angle , A}) is _____
a) sine of angle A
b) cosec of angle A
c) tan of angle A
d) cot of angle A
Answer: b
Clarification: The formula for cosec A is (frac {Length , of , hypotenuse , of , the , triangle}{Length , of , opposite , side , to , angle , A}).
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