Inverse Trigonometric Functions quiz

The principal value of cos^-1(-1/2) is:

The range of sin^-1 x is:

The domain of cos^-1 x is:

The domain of tan^-1 x is:

The value of sin^-1(sin(2pi/3)) is:

The value of tan^-1(sqrt(3)) - sec^-1(-2) is:

The principal value of cosec^-1(-sqrt(2)) is:

The principal value of tan^-1(-1) is:

The range of cot^-1 x is:

The principal value of sec^-1(2) is:

Find the principal value of cot^-1(-1). (2 marks)

Find the principal value of sec^-1(-2). (2 marks)

Find the value of cos^-1(cos(7pi/6)). (2 marks)

Find the domain of sin^-1(x - 1). (2 marks)

Find the value of sin^-1(1/2) + cos^-1(1/2). (2 marks)

Evaluate tan(sin^-1(1/2)). (2 marks)

Find the value of tan^-1(tan(3pi/4)). (2 marks)

What is the range of sec^-1 x? Why is pi/2 excluded? (2 marks)

Find the principal value of cosec^-1(2). (2 marks)

Evaluate cos(tan^-1(3/4)) using a right triangle. (2 marks)

Find the value of tan^-1(1) + cos^-1(-1/2) + sin^-1(-1/2). (3 marks)

Evaluate (i) sin^-1(sin(3pi/5)) and (ii) cos^-1(cos(13pi/6)). (3 marks)

Find the domain and range of f(x) = cos^-1(2x - 1). (3 marks)

Evaluate sin(tan^-1(3/4)) + cos(sin^-1(5/13)). (3 marks)

Find the value of cos^-1(1/2) + 2 sin^-1(1/2). (3 marks)

Read the passage and answer the questions. A girl standing 30 sqrt(3) m from the foot of a 30 m tall building looks at its top. The angle of elevation is given by theta = tan^-1(30/(30 sqrt(3))). (i) Find theta. (ii) If she walks 20 sqrt(3) m closer, write the new angle as an inverse tangent. (iii) Find the new angle. (5 marks)

Read the passage and answer the questions. A wheelchair ramp rises 1 m over a horizontal distance of sqrt(3) m. The angle of the ramp with the ground is alpha. (i) Express alpha as an inverse trigonometric function. (ii) Find alpha in radians. (iii) Express alpha using sin^-1. (5 marks)

Read the passage and answer the questions. Two students argue about sin^-1(sin(5pi/6)). Ravi says it is 5pi/6 and Meena says it is pi/6. (i) Who is correct? (ii) Explain why. (iii) Find cos^-1(cos(5pi/3)). (5 marks)

Read the passage and answer the questions. A teacher asks the class to restrict y = cos x to make it invertible. One student chooses [0, pi] and another chooses [pi, 2pi]. (i) Are both restrictions valid? (ii) Which is the principal branch? (iii) Find cos^-1(0) on the principal branch. (5 marks)

Read the passage and answer the questions. A searchlight on a lighthouse 50 m high shines on a boat. When the boat is 50 m away, the angle of depression is theta1; when it is 50 sqrt(3) m away, it is theta2. (i) Write theta1 and theta2 using tan^-1. (ii) Find their values. (iii) Find theta1 - theta2. (5 marks)

State the domain and range of all six inverse trigonometric functions (principal branches) and draw the graphs of sin^-1 x and cos^-1 x. (6 marks)

Draw the graph of y = tan^-1 x and y = cot^-1 x, showing their asymptotes and ranges. (6 marks)

Evaluate (i) sin^-1(sin(7pi/6)), (ii) cos^-1(cos(4pi/3)), (iii) tan^-1(tan(5pi/6)), explaining each step. (6 marks)

Find the principal values of sin^-1(-sqrt(3)/2), cos^-1(-sqrt(3)/2), tan^-1(1/sqrt(3)), cosec^-1(-2), sec^-1(2/sqrt(3)) and cot^-1(sqrt(3)). (6 marks)

Explain with a graph how the graph of y = sin^-1 x is obtained from y = sin x by reflection in the line y = x. Why is it necessary to restrict the domain first? (6 marks)