Trigonometry Test

Result

Trigonometry Test - 2

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
3 / -1

Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for "Trigonometry" under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.

Q. 3sinx + 4cosx + r is always greater than or equal to 0. What is the smallest value ‘r’ can to take?

A
5

B
-5

C
4

D
3

Solution
Question 2
3 / -1

Sin²⁰¹⁴x + Cos²⁰¹⁴x = 1, x in the range of [-5π, 5π], how many values can x take?

A
0

B
10

C
21

D
11

Solution

We know that Sin²x + Cos²x = 1 for all values of x.
If Sin x or Cos x is equal to –1 or 1, then Sin²⁰¹⁴x + Cos²⁰¹⁴x will be equal to 1.

Sin x is equal to –1 or 1 when x = –4.5π or –3.5π or –2.5π or –1.5π or –0.5π or 0.5π or 1.5π or 2.5π or 3.5π or 4.5π.
Cosx is equal to –1 or 1 when x = –5π or –4π or –3π or –2π or –π or 0 or π or 2π or 3π or 4π or 5π.

For all other values of x, Sin²⁰¹⁴ x will be strictly lesser than Sin²x.
For all other values of x, Cos²⁰¹⁴ x will be strictly lesser than Cos²x.

We know that Sin²x + Cos²x is equal to 1. Hence, Sin²⁰¹⁴x + Cos²⁰¹⁴x will never be equal to 1 for all other values of x. Thus there are 21 values.
Answer choice (C)
Question 3
3 / -1

Consider a regular hexagon ABCDEF. There are towers placed at B and D. The angle of elevation from A to the tower at B is 30 degrees, and to the top of the tower at D is 45 degrees. What is the ratio of the heights of towers at B and D?

A

B

C

D

Solution

Let the hexagon ABCDEF be of side ‘a’. Line AD = 2a. Let towers at B and D be B’B and D’D respectively.
From the given data we know that ∠B´AB = 30° and ∠D´AB = 45°. Keep in mind that the Towers B’B and D´D are not in the same plane as the hexagon.
Question 4
3 / -1

Find the maximum and minimum value of 8 cos A + 15 sin A + 15

A
11√2+15; 15

B
30; 8

C
32; -2

D
23; 8

Solution
Question 5
3 / -1

If cos A + cos² A = 1 and a sin¹² A + b sin¹⁰ A + c sin⁸ A + d sin⁶ A - 1 = 0. Find the value of

A
4

B
3

C
6

D
1

Solution

Given,
Cos A = 1- Cos²A
=) Cos A = Sin² A
=) Cos²A = Sin⁴A
=) 1 – Sin² A = Sin⁴ A
=) 1 = Sin⁴ A + Sin² A
=) 1³ = (Sin⁴A + Sin²A)³
=) 1 = Sin¹² A + Sin⁶A + 3Sin⁸ A + 3Sin¹⁰ A
=) Sin¹² A + Sin⁶A + 3Sin⁸ A + 3Sin¹⁰ A – 1 = 0
On comparing,
a = 1, b = 3 , c = 3 , d = 1
Question 6
3 / -1

In the above figure, the sheet of width W is folded along PQ such that R overlaps S Length of PQ can be written as :-

A

B

C

D
Any two of the above

Solution

If you are quick at observing , this question can be solved just by looking at the options as ,

We can draw the figure as :-

Answer choice (D)
Question 7
3 / -1

Find the value of :- (log sin 1° + log sin 2° ………..+ log sin 89°) + (log tan 1° + log tan 2° + ……… + log tan 89°) - (log cos 1° + log cos 2° + ……… + log cos 89°)

A
log √2/(1+√2)

B
-1

C
1

D
none of these

Solution

Writing the equation as :-

(log sin 1° - log cos 89°) + (log sin 2° - log cos 88°) + (log sin 3° - log cos 87°)………… + log tan 1°. log tan 89° + log tan 2°. log tan 88° + …….

=) (log sin 1° - log sin 1°) +(log sin 2° - log sin 2°)+……..+ log tan 1°cot 1° + log tan 2°cot 2°

=) log 1 = 0
Question 8
3 / -1

Ram and Shyam are 10 km apart. They both see a hot air balloon passing in the sky making an angle of 60° and 30° respectively. What is the height at which the balloon could be flying?

A

B
5√3

C
Both A and B

D
Can’t be determined

Solution
Question 9
3 / -1

A man standing on top of a tower sees a car coming towards the tower. If it takes 20 minutes for the angle of depression to change from 30° to 60°, what is the time remaining for the car to reach the tower?

A
20√3 minutes

B
10 minutes

C
10√3 minutes

D
5 minutes

Solution
Question 10
3 / -1

A right angled triangle has a height ‘p’, base ‘b’ and hypotenuse ‘h’. Which of the following value can h² not take, given that p and b are positive integers?

A
74

B
52

C
13

D
23

Solution

We know that,
h² = p² + b² Given, p and b are positive integer, so h2 will be sum of two perfect squares. We see
a) 72 + 52 = 74
b) 62 + 42 = 52
c) 32 + 22 = 13
d) Can’t be expressed as a sum of two perfect squares
The question is "Which of the following value can h2 not take, given that p and b are positive integers? "
Hence, the answer is 23