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
View Answer

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

Answer: c
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) ∞
View Answer

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

Answer: a
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
View Answer

Answer: a
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.
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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°
View Answer

Answer: c
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
View Answer

Answer: a
Explanation: Cosec 0° = \(\frac {1}{Sin \, ⁡0^{\circ } } = \frac {1}{0}\)
Any number divided with 0 is always not defined.
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8. The value of sin 90° + cos 0° + √2 cos 45° is_____
a) 2
b) 1
c) 4
d) 3
View Answer

Answer: d
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
View Answer

Answer: c
Explanation: Cosec 90° = \(\frac {1}{Sin \, ⁡90^{\circ } }\)
= \(\frac {1}{1}\)
= 1
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10. \(\frac {Cos \, ⁡0^{\circ }}{1 – Sin \, ⁡30^{\circ }}\) is _____
a) 1
b) 2
c) 3
d) 4
View Answer

Answer: b
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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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter