Trigonometry - Aptitude Questions and Answers

View in English View in Hindi

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

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

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

Latest Updates

Area

If the area of a square is 16 cm2, then the area of the square joining the mid-points of the sides is?

General Knowledge of MP

Vidisha is situated on the banks of river?

General Knowledge of World

When is the Human Rights Day celebrated?

Profit and Loss

By selling coconuts at the rate of Rs. 6/- each, a trader gained 20%. Find the cost of 100 coconuts?

General Knowledge of India

How many coastal state are in India?

Numbers

A person is to count 4500 currency notes. Let an denote the number of notes he counts in the nth minute. If a1 = a2 = .... = a10 = 150 and a10 , a11 ,... are in an AP with common difference – 2, then the time taken by him to count all notes is ?

The value of product 6 1/2 * 6 1/4 * 6 1/8 * 6 1/16 * -----∞ upto infinite terms?

Unix/Linux

What is nohup command in unix?

How do display the 10th, 11th and 12th line of a file in Unix?

Average

The mean of 100 students marks was found to be 40. it was found later that a mark 53 was read as 83. the correct mean is?

Numbers

The geometric mean of three observations 40, 50 and X is 10, then the value of X is ?

Indian Politics

Who appoints the members of National human rights commission?

The President of India can resign by writing under his hand addressed to?

Under which article of the constitution of India can the President of India refer a matter to the Supreme Court for its opinion?

General Computer Knowledge

The term VPN stands for ?

The transmission control protocol(TCP) is a............ layer protocol ?

Oracle PL/SQL

What is the difference between Procedure and Function?

Define exception and How will you raise an exception in PL/SQL procedure?