Mathematics Questions and Answers – Trigonometric Functions – 2

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This set of Mathematics Questions and Answers for Entrance exams focuses on “Trigonometric Functions – 2”.

1. cosec(-30°) =___________
a) -2
b) 2
c) 2/√3
d) -2/√3
View Answer

Answer: a
Explanation: We know, cosec(-x) = cosec x
So, cosec(-30°) = -cosec 30°=-2.
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2. sec(-45°) =_____________
a) 1
b) -1
c) √2
d) -√2
View Answer

Answer: c
Explanation: We know, sec(-x) = sec x
So, sec(-45°)=sec 45°=1/(cos 45°)=√2.

3. cot x is not defined for_______
a) 0
b) nπ/2
c) (2n+1) π/2
d) nπ
View Answer

Answer: d
Explanation: We know, cot x is not defined when sin x = 0.
sin x = 0 whenever x is 0, π, 2π, 3π, …. i.e. all integral multiples of π
so, x=nπ.
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4. If sin x=-4/5 and x lies in 3rd quadrant, then find sec x.
a) 5/3
b) 3/5
c) -3/5
d) -5/3
View Answer

Answer: d
Explanation: sin x=-4/5
We know, sin2x + cos2x=1
cos2x = 1-(-4/5)2 = 1-16/25=9/25
cos x=±3/5
cos x is negative in 3rd quadrant so, cos x=-3/5.
sec x = 1/cos x = 1/(-3/5) = – 5/3.

5. If cosec x = -5/12 and x lies in 2nd quadrant, then find cos x.
a) 12/13
b) 5/13
c) -13/5
d) 12/13
View Answer

Answer: c
Explanation: cosec x = 5/12
sin x = 1/cosec x = 12/5
We know, sin2x+cos2x=1
cos2 x = 1-(-12/5)2 = 1+144/25 = 169/25
cos x = ±13/5
cos x is negative in 2nd quadrant so, cos x=-13/5.
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6. If sec x = 13/5 and x lies in 4th quadrant, then find cot x.
a) 5/12
b) -5/12
c) 5/13
d) -5/13
View Answer

Answer: b
Explanation: sec x = 13/5.
We know, sec2x – tan2x=1
tan2x = (13/5)2-1 = (169/25) – 1 = 144/25
tan x = ±12/5
tan x is negative in 4th quadrant so, tan x=-12/5
cot x = 1/tan x = 1/(-12/5) = – 5/12.

7. If tan x = -5/12 and x lies in 2nd quadrant, then find cosec x.
a) 12/5
b) 13/5
c) -13/5
d) -12/5
View Answer

Answer: b
Explanation: tan x = -5/12
cot x = 1/tan x = 1/ (-5/12) = -12/5
We know, cosec2x – cot2x = 1
cosec2x =1+(-12/5)2 = 1+144/25 = 169/25
cosec x = ± 13/5
cosec x is positive in 2nd quadrant so, cosec x = 13/5.
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8. sin (15π/6) =_____________
a) 1
b) -1
c) 0
d) 1/2
View Answer

Answer: a
Explanation: sin(15π/6) = sin (2π + 3π/6) = sin (3π/6) {sin(2nπ+x)=sin x}
= sin (π/2) = 1.

9. cos (17π/3) =______________
a) 1/2
b) -1/2
c) √3/2
d) -√3/2
View Answer

Answer: a
Explanation: cos (17π/3) = cos (2π*3 – π/3)
{cos (2nπ-x)=cos x}
= cos(π/3) = 1/2.
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10. tan (19π/6) =____________________
a) √3
b) -1/√3
c) – √3
d) 1/√3
View Answer

Answer: d
Explanation: tan (19π/6) = tan (2π + 7π/6) = tan 7π/6 {tan( 2nπ+x)=tan x}
= tan (π+π/6) = tan π/6 = 1/√3. {tan π+x = tan x}

11. cos ( -1500°) =______________
a) 1/2
b) -1/2
c) √3/2
d) -√3/2
View Answer

Answer: a
Explanation: cos(-1500°) = cos(1500°) {cos(-x) = cos x}
= cos (4*360° + 60°) = cos 60° = 1/2. {cos (2nπ+x) = cos x}

12. sin 1710° =__________________
a) 1
b) -1
c) 0
d) 1/2
View Answer

Answer: b
Explanation: sin 1710° = sin (360°*5 – 90°) {sin (2nπ-x)= – sin x}
=-sin 90° = -1.

13. tan 1560°=_________________
a) -√3
b) √3
c) 1/√3
d) -1/√3
View Answer

Answer: a
Explanation: tan 1560° = tan (360°*4 + 120°) = tan 120° {tan (2nπ+x) = tan x}
= tan (180°-60°) = -tan 60° = – √3. {tan π-x = – tan x}

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter