# Mathematics Questions and Answers – Trigonometric Ratios of Specific Angles – 1

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Trigonometric Ratios of Specific Angles – 1”.

1. What is the value of sec θ when θ is 45°?
a) √3
b) 1
c) 0
d) √2

Explanation: The value of cos 45° is $$\frac {1}{\sqrt 2}$$ and secant is inverse to cos.
So, sec θ = $$\frac {1}{cos \, \theta } = \frac {1}{1/\sqrt 2}$$
= √2

2. What is the value of sin 0° + cos 0°?
a) 0
b) 2
c) 1
d) ∞

Explanation: The value of sin 0° is 0 and the value of cos 0° is 1.
sin 0° + cos 0° = 0 + 1
= 1

3. Evaluate cos 30° sin 60° + cos 60° sin 30°.
a) 2
b) 0
c) 1
d) ∞

Explanation: cos 30° sin 60° + cos 60° sin 30° = $$\frac {\sqrt 3}{2} . \frac {\sqrt {3}}{2} + \frac {1}{2} . \frac {1}{2}$$
= $$\frac {3 + 1}{4}$$
= $$\frac {4}{4}$$
= 1

4. What is the value of cos (30° + 60°)?
a) 1
b) $$\frac {1}{4}$$
c) $$\frac {3}{4}$$
d) 0

Explanation: cos (30° + 60°) = cos (90°) = 1
The value of cos (90°) is 1

5. 60° lies in the_____ quadrant.
a) first
b) second
c) third
d) fourth

Explanation: A plane is divided into four quadrants. The first quadrant ranges from 0° to 90°. So, 60° lies between 0° to 90° which is in the first quadrant of a plane.

6. What is the value of $$\frac {2 cot \, ⁡60^{\circ }}{1 + cot \, ⁡⁡45^{\circ }}$$?
a) Cot 30°
b) Cot 45°
c) Cot 60°
d) Tan 60°

Explanation: $$\frac {2 cot \, ⁡⁡60^{\circ }}{1 + cot \, ⁡⁡45^{\circ }} = \frac {2 (\frac {1}{\sqrt 3})}{1 + 1}$$
= $$\frac {\frac {2}{\sqrt {3}}}{2}$$
= $$\frac {1}{\sqrt 3}$$
= Cot 60°

7. Cosec 0° is _____
a) Not defined
b) 1
c) 0
d) 2

Explanation: Cosec 0° = $$\frac {1}{Sin \, ⁡0^{\circ } } = \frac {1}{0}$$
Any number divided with 0 is always not defined.

8. The value of sin 90° + cos 0° + √2 cos 45° is_____
a) 2
b) 1
c) 4
d) 3

Explanation: sin 90° + cos 0° + √2 cos 45° = 1 + 1 + √2 ($$\frac {1}{\sqrt {2}}$$)
= 1 + 1 + 1
= 3

9. Cosec 90° is _____
a) 0
b) 2
c) 1
d) √3

Explanation: Cosec 90° = $$\frac {1}{Sin \, ⁡90^{\circ } }$$
= $$\frac {1}{1}$$
= 1

10. $$\frac {Cos \, ⁡0^{\circ }}{1 – Sin \, ⁡30^{\circ }}$$ is _____
a) 1
b) 2
c) 3
d) 4

Explanation: $$\frac {Cos \, ⁡0^{\circ }}{1 – Sin \, ⁡30^{\circ }} = \frac {1}{1 – 1/2}$$
= $$\frac {1}{1/2}$$
= 2

Sanfoundry Global Education & Learning Series – Mathematics – Class 10.

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