Trigonometry - Aptitude Questions and Answers

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If x = a cosθ + b sinθ and y = a sinθ - b cosθ then what is x2 + y2 equal to?

A)

2ab


B)

a + b


C)

a2 + b2


D)

a2 - b2



Correct Answer :

a2 + b2


Explanation :

x2 + y2 = (a cosθ + b sinθ)2 + (a sinθ - b cosθ)2
= (a2 cos2θ + b2 sin2θ + 2*ab* cosθ*sinθ) + (a2 cos2θ + b2 sin2θ - 2*ab* cosθ*sinθ)
= (a2 cos2θ + b2 sin2θ + a2 cos2θ + b2 sin2θ )
= a2(cos2θ + sin2θ) + b2 (cos2θ + sin2θ)​​​​​​​
= a2+ b2

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What is the value of cot 4π/3 ?

A)

1/√3


B)

-√3


C)

-1


D)

√3



Correct Answer :

1/√3


Explanation :

cot 4π/3
= cos 4π/3 / sin 4π/3
= -1/2 / -√3/2
= 1/√3

What is the value of sinx √( 1 /1+cosx + 1 /1-cosx ) ?

A)

√2


B)

2√2


C)

√2 tanx


D)

0



Correct Answer :

√2


Explanation :

sinx √( 1 /1+cosx + 1 /1-cosx )
=sinx √( 1-cosx + 1+cosx / (1+cosx ) (1-cosx) )
=sinx √( 2 / (1 - cos2x ) )
=sinx √ (2 / sin2x)
=sinx √ 2 / sinx
=√ 2

What is cos4 A - sin4 A / cos2 A - sin2 A equal to?

A)

cos2 A - sin2 A


B)

cos A - sin A


C)

1


D)

2



Correct Answer :

1


Explanation :

cos4 A - sin4 A / cos2 A - sin2 A
= (cos2 A)2 - (sin2 A)2 / cos2 A - sin2 A
= (cos2 A + sin2 A) (cos2 A - sin2 A) / (cos2 A - sin2 A)
= (cos2 A + sin2 A) (cos2 A - sin2 A) / (cos2 A - sin2 A)
= (cos2 A + sin2 A)
​​​​​​​​​​​​​​= 1

If 7sin2 x +3cos2 x = 4, 0 < x < 90º ,then what is the value of tan x?

A)

√2


B)

1


C)

√3/2


D)

1/√3



Correct Answer :

1/√3


Explanation :

7sin2 x +3cos2 x = 4
7sin2 x/cos2 x + 3cos2 x/cos2 x = 4/cos2 x
7tan2 x + 3 = 4sec2 x
​​​​​​​7tan2 x + 3 = 4(1+tan2 x)
​​​​​​​​​​​​​​3tan2 x = 1
​​​​​​​​​​​​​​tan x = 1/√3

2 tan 45° /( 1+ tan2 45°) = ?

A)

sin 90°


B)

tan 30°


C)

tan 90°


D)

sin 45°



Correct Answer :

sin 90°


Explanation :

2 tan 45° /( 1+ tan2 45°)
= 2 / (1 + 12) (tan 45°=1)
= 1
= sin 90°

If sinA= 8/17 and cosA=15/17, then cotA=?

A)

17/8


B)

8/15


C)

17/15


D)

15/8



Correct Answer :

15/8


Explanation :

As given sinA = 8/17 = perpendicular/hypotenuse
cosA= 15/17 = base/hypotenuse

tanA = sinA/cosA = perpendicular/base = 8/15
cotA = 1/tanA = base/perpendicular = 15/8

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