Mathematics Multiple Choice Questions & Answers on “Trigonometric Ratios of Complementary Angles – 1”.
1. Which among these are complementary angles?
a) ∠A + ∠B = 90°
b) ∠A + ∠B = 180°
c) ∠A + ∠B = 60°
d) ∠A + ∠B = 45°
Answer: a
Clarification: Two angles are said to be complementary angles if the sum of these two angles is 90° but if the sum of these two angles is 180° then these two angles are said to be supplementary.
2. The sum of two angles in ∆PQR is complementary with the right angle at Q.
a) True
b) False
Answer: a
Clarification: ∠P + ∠Q + ∠R = 180° ( ∵ The sum of angles in a triangle is 180°)
∠P + 90° + ∠R = 180°
∠P + ∠R = 180° – 90°
∠P + ∠R = 90°
Two angles are said to be complementary angles if the sum of these two angles is 90°.
3. Which trigonometric ratios are positive in the second quadrant?
a) Cosec, Sin
b) Sec, Tan
c) Sin, Cot
d) Tan, Cot
Answer: a
Clarification: A plane is divided into four infinite quadrants. The trigonometric ratios that are positive in the second quadrant are sine, cosecant and the rest of all trigonometric ratios are negative in this quadrant.
4. Sin (90° – x) equals to ______
a) cos x
b) cot x
c) cosec x
d) sec x
Answer: a
Clarification: (90° – x) refers to the first quadrant which lies in the range from 0° to 90°. All trigonometric ratios are positive in the first quadrant and sine changes to cosine when it is 90° or 270°.
5. What is the value of tan 48°?
a) Cot 42°
b) Tan 42°
c) Tan 16°
d) Cot 16°
Answer: a
Clarification: All trigonometric ratios are positive in the first quadrant and tan changes to cot when it is 90° or 270°.
Tan 48° = Tan (90° – 42°)
= Cot 42°
6. Sec 75° equals to _____
a) cosec 15°
b) sec 15°
c) 1
d) 0
Answer: a
Clarification: All trigonometric ratios are positive in the first quadrant and secant changes to cosecant when it is 90° or 270°.
Sec 75° = Sec (90° – 15°)
= Cosec 15°
7. Evaluate (frac {Cot , 54^{circ }}{tan , 36^{circ }}).
a) 0
b) 1
c) (frac {4}{3})
d) (frac {3}{4})
Answer: b
Clarification: (frac {Cot , 54^{circ }}{tan , 36^{circ }} = frac {Cot , (90^{circ }-36^{circ })}{tan , 36^{circ }} )
= (frac {tan , 36^{circ }}{tan , 36^{circ }} )
= 1
8. Find the value of cos 135°.
a) (frac {1}{sqrt {2}})
b) √2
c) -√2
d) (frac {-1}{sqrt {2}})
Answer: d
Clarification: Cos 135° = Cos (90° + 45°)
= -Sin 45°
= (frac {-1}{sqrt {2}})
9. Evaluate tan 75° + cot 65°.
a) Cot 25° + Tan 15°
b) Cot 25° – Tan 15°
c) Cot 15° + Tan 25°
d) Cot 15° – Tan 25°
Answer: c
Clarification: Tan 75° + Cot 65° = Tan (90° – 15°) + Cot (90° – 25°)
= Cot 15° + Tan 25°
10. Cot(180° – a) is _____
a) sine of angle A
b) -cosec of angle A
c) tan of angle A
d) -cot of angle A
Answer: b
Clarification: (180° – a) refers to the second quadrant which lies in the range from 90° to 180°. Trigonometric ratios sine and cosec are only positive in the second quadrant and remaining all the trigonometric ratios are negative.
So, Cot (180° – a) = -Cot A