Mathematics Questions and Answers – Trigonometric Ratios of Specific Angles – 2

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This set of Mathematics Written Test Questions and Answers for Class 10 focuses on “Trigonometric Ratios of Specific Angles – 2”.

1. What is the value of tan θ when θ is 30°?
a) \( \frac {1}{\sqrt 3}\)
b) 1
c) 0
d) 2
View Answer

Answer: a
Explanation: Tan θ = \( \frac {Sin \, \theta}{Cos \, \theta} = \frac {Sin \, 30^{\circ }}{Cos \, 30^{\circ }} \)
= \( \frac {1/2}{\sqrt 3/2}\)
= \( \frac {1}{2} \times \frac {2}{\sqrt 3}\)
= \( \frac {1}{\sqrt 3}\)
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2. What is the value of sec 0° + cosec 90°?
a) 0
b) 2
c) 1
d) ∞
View Answer

Answer: b
Explanation: The value of sec 0° is 1 and the value of cosec 90° is 1.
sec 0° + cosec 90° = 1 + 1
= 2

3. Evaluate sin2 30.
a) 2
b) 0
c) \( \frac {1}{4}\)
d) ∞
View Answer

Answer: c
Explanation: Sin2 30° = (\( \frac {1}{2}\))2
= \( \frac {1}{4}\)
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4. What is the value of cos 45° + sin 45°?
a) 1
b) \( \frac {1}{4}\)
c) \( \frac {3}{4}\)
d) √2
View Answer

Answer: d
Explanation: cos 45° + sin 45° = \( \frac {1}{\sqrt 2} + \frac {1}{\sqrt 2}\)
= 2 × \( \frac {1}{\sqrt 2}\) ( Since, 2 = √2 × √2 )
= √2

5. 135° lies in the third quadrant.
a) True
b) False
View Answer

Answer: b
Explanation: A plane is divided into four quadrants. The second quadrant ranges from 90° to 180°. So, 135° lies between 90° to 180° which is in the second quadrant of a plane not in the third quadrant.
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6. What is the value of sec 60° – \( \frac {1}{cosec \, 90^{\circ }}\)?
a) Cot 30°
b) Cot 45°
c) Cot 60°
d) Tan 60°
View Answer

Answer: b
Explanation: sec 60° – \( \frac {1}{cosec \, 90^{\circ }}\) = 2 – \( \frac {1}{1}\)
= 1
= cot 45°

7. Tan 90° is _____
a) Not defined
b) 1
c) 0
d) 2
View Answer

Answer: a
Explanation: Tan 90° = \(\frac {Sin \, 90^{\circ }}{Cos \, 90^{\circ }} = \frac {1}{0}\)
Any number divided with 0 is always not defined.
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8. The value of sin2 90° + √2 cos 45° + √3 cot 30° is_____
a) 2
b) 0
c) 4
d) 5
View Answer

Answer: d
Explanation: sin2 90° + √2 cos 45° + √3 cot 30° = 12 + √2 (\( \frac {1}{\sqrt 2}\)) + √3 (√3)
= 1 + 1 + 3
= 5

9. The product of sec 30° and cos 60° is _____
a) 0
b) 2
c) 1
d) \( \frac {1}{\sqrt 3}\)
View Answer

Answer: d
Explanation: (sec 30°) (cos 60°) = \(( \frac {2}{\sqrt 3}) ( \frac {1}{2} )\)
= \( \frac {1}{\sqrt 3}\)
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10. \( \frac {1 – cot \, 45^{\circ}}{1+ cot \, 45^{\circ}}\) is _____
a) 0
b) 2
c) 3
d) 1
View Answer

Answer: a
Explanation: \( \frac {1 – cot \, 45^{\circ}}{1 + cot \, 45^{\circ}} = \frac {1-1}{1+1}\)
= \( \frac {0}{1}\)
= 0

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