INVERSES OF SIN COS AND TAN WORKSHEET

Questions 1-5 : If θ is an acute angle, find the value of θ in degrees.

Question 1 :

sinθ = 1/2

Question 2 :

tanθ = √3

Question 3 :

cosθ = √2/2

Question 4 :

sinθ = √2/2

Question 5 :

cosθ = √3/2

Questions 6-10 : If θ is an acute angle, find the value of θ in radians.

Question 6 :

sinθ = √3/2

Question 7 :

cosθ = 1/2

Question 8 :

tanθ = √3/3

Question 9 :

tanθ = 1

Question 10 :

tanθ = 1/0

1. Answer :

sinθ = 1/2

θ = sin^-1(1/2) ----(1)

From the table above, we have

sin30° = 1/2

30° = sin^-1(1/2) ----(2)

From (1) and (2),

θ = 30°

2. Answer :

tanθ = √3

θ = tan^-1(√3) ----(1)

From the table above, we have

tan60° = √3

60° = tan^-1(√3) ----(2)

From (1) and (2),

θ = 60°

3. Answer :

cosθ = √2/2

θ = cos^-1(√2/2) ----(1)

From the table above, we have

45° = cos^-1(√2/2) ----(2)

From (1) and (2),

θ = 45°

4. Answer :

sinθ = √2/2

θ = sin^-1(√2/2) ----(1)

From the table above, we have

sin45° = √2/2

45° = sin^-1(√2/2) ----(2)

From (1) and (2),

θ = 45°

5. Answer :

cosθ = √3/2

θ = cos^-1(√3/2) ----(1)

From the table above, we have

cos30° = √3/2

30° = cos^-1(√3/2) ----(2)

From (1) and (2),

θ = 30°

6. Answer :

sinθ = √3/2

θ = sin^-1(√3/2) ----(1)

From the table above, we have

sin60° = √3/2

60° = sin^-1(√3/2) ----(2)

From (1) and (2),

θ = 60°

To convert degrees to radians, multiply by π/180°.

θ = 60° ⋅ (π/180°)

θ = π/3

7. Answer :

cosθ = 1/2

θ = cos^-1(1/2) ----(1)

From the table above, we have

cos60° = 1/2

60° = cos^-1(1/2) ----(2)

From (1) and (2),

θ = 60°

To convert degrees to radians, multiply by π/180°.

θ = 60° ⋅ (π/180°)

θ = π/3

8. Answer :

tanθ = √3/3

θ = tan^-1(√3/3) ----(1)

From the table above, we have

tan30° = √3/3

30° = tan^-1(√3/3) ----(2)

From (1) and (2), 

θ = 30°

To convert degrees to radians, multiply by π/180°.

θ = 30° ⋅ (π/180°)

θ = π/6

9. Answer :

tanθ = 1

θ = tan^-1(1) ----(1)

From the table above, we have

45° = tan^-1(1) ----(2)

From (1) and (2),

θ = 45°

To convert degrees to radians, multiply by π/180°.

θ = 45° ⋅ (π/180°)

θ = π/4

10. Answer :

tanθ = 1/0

θ = tan^-1(1/0) ----(1)

From the table above, we have

tan90° = not defined

tan90° = 1/0

 90° = tan-1(1/0) ----(2)

From (1) and (2),

θ = 90°

To convert degrees to radians, multiply by π/180°.

θ = 90° ⋅ (π/180°)

θ = π/2

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