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

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.

2. Which value is similar to sin^{-1}sin(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

Explanation: sin

^{-1}sin(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

^{-1}sin(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

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)

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

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

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)

6. The given graph is for which equation?

a) y = sinx

b) y = sin^{-1}x

c) y = cosecx

d) y = secx

View Answer

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

^{-1}x

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^{-1}x

b) secx

c) cos^{-1}x

d) cotx

View Answer

Explanation: There are 2 curves.

The green curve is the graph of y = cosx

The red curve is the graph for y = cos

^{-1}x

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.

8. The given graph is for which equation?

a) y = cos^{-1}x

b) y = cot^{-1}x

c) y = cosec^{-1}x

d) y = tan^{-1}x

View Answer

Explanation: There are 2 curves.

The blue curve is the graph of y = tanx

The red curve is the graph for y = tan

^{-1}x

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^{-1}x

b) y = tan^{-1}x

c) y = cotx

d) y = cosec^{-1}x

View Answer

Explanation: There are 2 curves.

The black curve is the graph of y = cotx

The red curve is the graph for y = cot

^{-1}x

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.

10. The given graph is for which equation?

a) y = sinx

b) y = log|sinx|

c) y = |sinx|

d) y = |cosx|

View Answer

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.

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