Mathematics Multiple Choice Questions & Answers 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
Answer: d
Clarification: 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) ∞
Answer: c
Clarification: 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) ∞
Answer: c
Clarification: 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
Answer: a
Clarification: 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
Answer: a
Clarification: 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°
Answer: c
Clarification: (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
Answer: a
Clarification: 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
Answer: d
Clarification: 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
Answer: c
Clarification: 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
Answer: b
Clarification: (frac {Cos , 0^{circ }}{1 – Sin , 30^{circ }} = frac {1}{1 – 1/2})
= (frac {1}{1/2})
= 2