Mathematics Questions and Answers – Inverse Trigonometry

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Inverse Trigonometry”.

1. What will be the value of x + y + z if cos-1 x + cos-1 y + cos-1 z = 3π?
a) -1/3
b) 1
c) 3
d) -3
View Answer

Answer: d
Explanation: The equation is cos-1 x + cos-1 y + cos-1 z = 3π
This means cos-1 x = π, cos-1 y = π and cos-1 z = π
This will be only possible when it is in maxima.
As, cos-1 x = π so, x = cos-1 π = -1 similarly, y = z = -1
Therefore, x + y + z = -1 -1 -1
So, x + y + z = -3.
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2. Which value is similar to sin-1sin(6 π/7)?
a) sin-1(π/7)
b) cos-1(π/7)
c) sin-1(2π/7)
d) coses-1(π/7)
View Answer

Answer: a
Explanation: sin-1sin(6 π/7)
Now, sin(6 π/7) = sin(π – 6 π/7)
= sin(2π + 6 π/7) = sin(π/7)
= sin(3π – 6 π/7) = sin(20π/7)
= sin(-π – 6 π/7) = sin(-15π/7)
= sin(-2π + 6 π/7) = sin(-8π/7)
= sin(-3π – 6 π/7) = sin(-27π/7)
Therefore, sin-1sin(6 π/7) = sin-1(π/7).

3. What is the value of sin-1(-x) for all x belongs to [-1, 1]?
a) -sin-1(x)
b) sin-1(x)
c) 2sin-1(x)
d) sin-1(-x)/2
View Answer

Answer: a
Explanation: Let, θ = sin-1(-x)
So, -π/2 ≤ θ ≤ π/2
=> -x = sinθ
=> x = -sinθ
=> x = sin(-θ)
Also, -π/2 ≤ -θ ≤ π/2
=> -θ = sin-1(x)
=> θ = -sin-1(x)
So, sin-1(-x) = -sin-1(x)
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4. What is the value of sin-1(sin 6)?
a) -2π – 6
b) 2π + 6
c) either -2π + 6 or 2π + 6
d) 2π – 6
View Answer

Answer: c
Explanation: We know that sin(x) = sin(2A * π + x) where A can be positive or negative integer.
If A is -1, then sin(6) = sin(-2π + 6);
If A is 1, then sin(6) = sin(2π + 6);

5. What is the value of cos-1(-x) for all x belongs to [-1, 1]?
a) cos-1(-x)
b) π – cos-1(x)
c) π – cos-1(-x)
d) π + cos-1(x)
View Answer

Answer: b
Explanation: Let, θ = cos-1(-x)
So, 0 ≤ θ ≤ π
=> -x = cosθ
=> x = -cosθ
=> x = cos(-θ)
Also, -π ≤ -θ ≤ 0
So, 0 ≤ π -θ ≤ π
=> -θ = cos-1(x)
=> θ = -cos-1(x)
So, cos-1(x) = π – θ
θ = π – cos-1(x)
=> cos-1(-x) = π – cos-1(x)
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6. The given graph is for which equation?

a) y = sinx
b) y = sin-1x
c) y = cosecx
d) y = secx
View Answer

Answer: b
Explanation: The following graph represents 2 equations.

The pink curve is the graph of y = sinx
The blue curve is the graph for y = sin-1x
This curve passes through the origin and approaches to infinity in both positive and negative axes.

7. The given graph is for which equation?

a) cosec-1x
b) secx
c) cos-1x
d) cotx
View Answer

Answer: c
Explanation: There are 2 curves.

The green curve is the graph of y = cosx
The red curve is the graph for y = cos-1x
This curve origin from some point before π/3 and approaches to infinity in both positive y axis by intersecting at a point near 1.5 in y axis.
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8. The given graph is for which equation?

a) y = cos-1x
b) y = cot-1x
c) y = cosec-1x
d) y = tan-1x
View Answer

Answer: d
Explanation: There are 2 curves.

The blue curve is the graph of y = tanx
The red curve is the graph for y = tan-1x
This curve passes through the origin and approaches to infinity in the direction of x axis only.
This graph lies below –x axis and above +x axis.

9. The given graph is for which equation?

a) y = cot-1x
b) y = tan-1x
c) y = cotx
d) y = cosec-1x
View Answer

Answer: a
Explanation: There are 2 curves.

The black curve is the graph of y = cotx
The red curve is the graph for y = cot-1x
This curve does not pass through the origin but approaches to infinity in the direction of x axis only.
The part of the curve that lies in the (x, y) coordinate gradually meets to the x-axis.
This graph lies above +x axis and –x axis.
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10. The given graph is for which equation?

a) y = sinx
b) y = log|sinx|
c) y = |sinx|
d) y = |cosx|
View Answer

Answer: c
Explanation: The given form of equation can be written as,

The green curve is the graph of y = sinx
The blue curve is the graph for y = |sinx|
As sinx is enclosed by a modulus so the curve that lies in the negative y axis will come to the positive y axis.

Sanfoundry Global Education & Learning Series – Mathematics – Class 12.

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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