 # Trigonometry Questions- with pdf for SSC, Bank, And Railway

In almost every competitive exam like SSC, Railway, CDS, FCI, etc 1-2 Trigonometry questions are always asked, and being simple questions, marks can be scored easily. The trigonometry topic is totally based on the right-angle triangle. Here we explain all the basic formulas used in trigonometry students can read them and practice some questions.

A 400+ questions Pdf is given below students can download it and do practice.

##### Trigonometric function :

In Triangle A B C b base h p hypotenuse Perpendicular q

Sin q = p/h , Cos q = b/h , Tan q = p/b , Cot q = b/p, Sec q = h/b and Cosec q = h/p

Sin q . Cosec q =1, Cos q . Sec q =1, Tan q . Cot q =1

Sin q = 1/Cosec q or, Cosec q = 1/Sin q

Cos q = 1/Sec q or, Sec q = 1/Cos q

Tan q = 1/Cot q or, Cot q = 1/Tan q

Tan q = Sin q/Cos q and Cot q = Cos q/ Sin q

##### Trigonometric Identities :

Sin2 q + Cos2 q = 1 or Sin2 q = 1 – Cos2 q or, Cos2 q = 1 – Sin2 q

Sec2 q – Tan2 q = 1 or, Sec2 q = 1 + Tan2 q or, Tan2 q = Sec2 q – 1

Cosec2 q – Cot2 q = 1 or, Cosec2 q = 1 + Cot2 q or, Cot2 q = Cosec2 q – 1

### Trigonometry Questions Some special formulas :

i. sin (– q ) = – sin q cosec (– q ) = – cosec q, Cos (– q ) = cos q sec (– q ) = sec q, tan (– q ) = – tan q cot (– q ) = –cot q

ii. sin (90° – q ) = cos q cos(90° – q ) = sin q, tan (90° – q ) = cot q cot (90° – q ) = tan q

sec (90° – q ) = cosec q cosec(90° – q ) = sec q

iii. sin (90°+ q ) = cos q cos(90°+ q ) = –sin q, tan (90° + q ) = –cot q cot (90°+ q ) = –tan q

sec (90°+ q ) = –cosec q cosec(90°+ q ) = sec q

iv. sin (180°– q ) = sin q cos(180°– q ) = –cos q, tan (180°– q ) = –tan q cot (180°– q ) = –cot q

sec (180°– q ) = –sec q cosec(180°– q ) = cosec q

v. sin(180° + q ) = –sin q, cos(180° + q ) = –cos q, sec(180° + q ) = –sec q, cosec(180° + q ) = –cosec q

cot(180° + q ) = cot q

tan(180° + q ) = tan q

vi. sin(270°– q ) = –cos q cos(270°– q ) =–sin q, tan(270°– q ) = cot q cot(270°– q ) = +tan q

cosec(270°– q ) = –sec q sec(270°– q ) = –cosec q

vii. sin(270°+ q ) = –cos q cos(270°+ q ) = sin q, tan(270°+ q ) = –cot q cot(270°+ q ) = –tan q

cosec(270°+ q ) = –sec q sec(270°+ q ) = cosec q

viii. sin(360°– q ) = –sin q cos(360°– q ) = cos q, tan(360°– q ) = –tan q cosec(360°– q ) = –cosec q

sec(360°– q ) = sec q cot(360°– q ) = –cot q

ix. sin(360°+ q ) = sin q cos(360°+ q ) = cos q, tan(360°+ q ) = tan q cot(360°+ q ) = cot q, sec(360°+ q ) = sec q

cosec(360°+ q ) = cosec q

###### Angle and its measurement
1. The degree measure of 1 radian (taking II = 22/7) is
(1) 57°61’22” (approx.) (2) 57°16’22” (approx.) (3) 57°22’16” (approx.) (4) 57°32’16” (approx.)
1. If sin (3x – 20°) = cos (3y + 20°), then the value of (x + y) is
(1) 20° (2) 30° (3) 40° (4) 45°
1. If sec (7q + 28°) = cosec (30° – 3q) then the value of q is
(1) (2) 5° (3) 60° (4) 9°
1. If cosec q – cot q =7/2, the value of cosec q is :
(1) 47/28 (2) 51/28 (3) 53/28 (4) 49/28
1. If sin 7x = cos 11x , then the value of tan 9x + cot 9x is
(1) 1 (2) 2 (3) 3 (4) 4
1. If tan q =4/3 , then the value of 3sin q + 2cos q/ 3sin q – 2cos q is
(1) 0.5 (2) –0.5 (3) 3.0 (4) –3.0
1. The value of tan 11° tan 17° tan 79° tan 73° is
(1)1/2 (2) 0 (3) 1 (4) 1/√2

8. If tan4 q + tan2 q = 1 then the value of cos4 q + cos2 q is

(1) 2 (2) 0 (3) 1 (4) –1

1. If sec (4x – 50°) = cosec (50° – x), then the value of x is
(1) 45° (2) 90° (3) 30° (4) 60°
1. A man 6 ft tall casts a shadow 4 ft long, at the same time when a flag pole casts a shadow 50 ft
long. The height of the flag pole is
(1) 80 ft (2) 75 ft (3) 60 ft (4) 70 ft
1. A vertical stick 12 cm long casts a shadow 8 cm long on the ground.
At the same time, a tower casts a shadow 40 m long on the ground. The height of the tower is
(1) 72 m (2) 60 m (3) 65 m (4) 70 m
1. A tower standing on a horizontal plane subtends a certain angle at a point 160 m apart from the foot
of the tower. On advancing 100 m towards it, the tower is found to subtend an angle twice as before.
The height of the tower is
(1) 80 m (2) 100 m (3) 160 m (4) 200 m
1. A ladder is placed along a wall such that its upper end is touching the top of the wall. The foot
of the ladder is 10 ft away from the wall and the ladder is making an angle of 60° with the
ground. When a man starts climbing on it, it slips and now ladder makes an angle of 30° with
the ground. How much did the ladder slip from the top of the wall?
(1) 12 ft (2) 20 ft (3) 7.32 ft (4) 18 ft
1. There are two vertical posts, one on each side of a road, just opposite to each other. One
post is108 meters high. From the top of this post, the angle of depression of the top and foot of
the other post is 30° and 60° respectively. The height of the other post (in meter) is
(1) 36 (2) 72 (3) 108 (4) 110
1. The angle of elevation of the top of a tower from two points A and B lying on the horizontal through
the foot of the tower are respectively 15° and 30°. If A and B are on the same side of the tower
and AB = 48 metres, then the height of the tower is:
(1) 24√3 metres (2) 24 metre (3) 24√2 metres (4) 96 metre

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