Mathematics Objective Questions and Answers for Class 10 on “Trigonometric Ratios of Complementary Angles – 2”.
1. The sum of two angles in ∆ABC is supplementary with the right angle at B.
a) False
b) True
Answer: a
Clarification: A triangle contains three angles and their sum should be equal to 180° but the definition of supplementary angles says that two angles can be supplementary angles if the sum of these two angles is 180°.
2. Two angles are said to be supplementary if the sum of these two angles is 180°.
a) False
b) True
Answer: b
Clarification: Two angles are said to be supplementary angles if the sum of these two angles is 180° but if the sum of these two angles is 90° then these two angles are said to be complementary.
3. Which trigonometric ratios are positive in the fourth quadrant?
a) Cos, Sin
b) Sec, Cos
c) Sin, Cot
d) Tan, Cot
Answer: b
Clarification: A plane is divided into four infinite quadrants. The trigonometric ratios that are positive in the fourth quadrant are secant, cosine and the rest of all trigonometric ratios are negative in this quadrant.
4. Sin (270° – x) equals to ______
a) -cos x
b) cot x
c) -cosec x
d) sec x
Answer: a
Clarification: (270° – x) refers to the third quadrant which lies in the range from 90° to 270°. Tan and cot are only positive in the third quadrant and sine changes to cosine when it is 90° or 270°.
Sin (270° – x) = -Cos x
5. What is the product of cot 42° and tan 48°?
a) Cot2 42°
b) Tan2 42°
c) 2Tan 16°
d) 2Cot 16°
Answer: a
Clarification: (Cot 42°) (Tan 48°) = (Cot 42°) Tan (90° – 42°)
= Cot 42° Cot 42°
= Cot2 42°
6. Cot 405° equals to _____
a) cosec 15°
b) sec 15°
c) 1
d) 0
Answer: c
Clarification: All trigonometric ratios are positive in the first quadrant.
So, Cot 405° = Cot (360° + 45°)
= Cot 45°
= 1
7. Evaluate (frac {sin , 54^{circ }}{cos , 36^{circ }}).
a) 0
b) 1
c) (frac {4}{3})
d) (frac {3}{4})
Answer: b
Clarification: (frac {sin , 54^{circ }}{cos , 36^{circ }} = frac {sin , (90^{circ }-36^{circ })}{cos , 36^{circ }})
= (frac {Cos , 36^{circ }}{Cos , 36^{circ }})
= 1
8. Find the value of tan 225°.
a) (frac {1}{sqrt 2})
b) 1
c) -√2
d) (frac {-1}{sqrt 2})
Answer: b
Clarification: Tan 225° = Tan (180° + 45°)
= Tan 45°
= 1
9. Evaluate sec 65° + cosec 75°.
a) Cosec 25° + Sec 15°
b) Cosec 25° – Sec 15°
c) Cosec 15° + Sec 25°
d) Cosec 15° – Sec 25°
Answer: c
Clarification: Sec 65° + Cosec 75° = Sec (90° – 25°) + Cosec (90° – 15°)
= Cosec 25° + sec 15°
10. Sec (360° – θ) is _____
a) sine of angle θ
b) secant of angle θ
c) tan of angle θ
d) cot of angle θ
Answer: b
Clarification: (360° – θ) refers to the fourth quadrant which lies in the range from 270° to 360°. Trigonometric ratios secant and cosine are only positive in the second quadrant and remaining all the trigonometric ratios are negative.
So, Sec (360° – θ) = Sec θ
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