SOLVING INVERSE TRIG FUNCTIONS WORKSHEET

Problem 1 :

The value of sin^-1 (cos x) = 0, 0 ⩽ x ⩽ π is

1) π - x     2)  x - (π/2)      3)  (π/2) - x       4)  x - π

Solution

Problem 2 :

If sin^-1 x + sin^-1y = 2π/3, then cos^-1 x + cos^-1y is equal to 

1) 2π/3     2)  π/3      3)  π/6       4)  π

Solution

Problem 3 :

Solution

Problem 4 :

If sin^-1 x = 2 sin^-1α has a solution, then

1) |α| ≤ 1/√2     2)  |α| ≤ 1/√2    3)  |α| < 1/√2      4)  |a| > 1/√2

Solution

Problem 1 :

sin^-1(cos x) = π/2 - x is valid for 

1)  -π ≤ x ≤ 0   b)  0 ≤ x ≤ π    3) -π/2 ≤ x ≤ π/2

4)  -π/4 ≤ x ≤ 3π/4

Solution

Problem 2 :

If cot^-1 x = 2π/5 for some x ∈ R, the value of tan^-1 x is 

1)  -π/10   b)  π/5    3) π/10     4)  -π/5

Solution

Problem 3 :

The domain of the function is defined by f(x) = sin^-1 √(x -1) is 

1)  [1, 2]   b)  [-1, 1]    3) [0, 1]     4)  [-1, 0]

Solution

Problem 4 :

If x = 1/5, the value of cos (cos^-1x + 2 sin^-1x) is 

1)  √(24/25)    b)  √24/25    3) (1/5)    4) (-1/5).

Solution

Problem 5 :

tan^-1(1/4) + tan^-1(2/9) is equal to

1)  √(24/25)    b)  √24/25    3) (1/2) tan^-1 (3/5)     4) tan^-1 (1/2)

Solution

Problem 6 :

If the function f(x) = sin^-1(x² - 3), then x belongs to

1)  [-1, 1]    b)  [√2, 2]    3) [-2, -√2] U [√2, 2]     4) [-2, -√2]

Solution

Problem 7 :

If cot^-1 2 and cot^-1 3 are two angles of a triangle, then the third angle is 

1)  π/4   b)  3π/4    3) π/6     4)  π/3

Solution

Problem 8 :

If sin^-1(tan π/4) - sin^-1√(3/x) = π/6. Then x is a root of the equation.

1) x² - x - 6 = 0   2)  x² - x - 12 = 0    3) x² + x - 12 = 0

     4)  x² + x - 6 = 0

Solution

Problem 9 :

Solution

Problem 10 :

Solution

Problem 11 :

If |x| ⩽1, then

Solution

Problem 12 :

The equation

1) no solution    2) Unique solution

3) two solution      4) infinite number of solutions

Solution

Problem 13 :

Solution

Problem 14 :

Solution

Problem 15 :

sin(tan^-1x), |x| < 1 is equal to

Solution