Trigonometric Identities Problems

1Knowing that cos α = ¼ , and that 270º < α < 360°, calculate the remaining trigonometric ratios of angle α.

2 Knowing that tan α = 2, and that 180º < α < 270°, calculate the remaining trigonometric ratios of angle α.

3 Knowing that sec α = 2 and 0 < α < /2, calculate the remaining trigonometric ratios of angle α.

4 Knowing that csc α = 3, calculate the remaining trigonometric ratios of angle α.

5Prove the identities:

1

2

3

4

5

6 Simplify the fractions:

1 

2 

3 

7Prove the identities:

1

2

8Simplify the fractions:

1

2

3

9 Calculate the trigonometric ratios of 15 (from the 45º and 30º).

10 Develop: cos(x+y+z).

11 Calculate sin 3x, depending on sin x.

12 Calculate sin x, cos x and tan x, in terms of tan x/2.

1

Knowing that cos α = ¼ , and that 270º <α <360°, calculate the remaining trigonometric ratios of angle α.

2

Knowing that tan α = 2, and that 180º < α <270°, calculate the remaining trigonometric ratios of angle α.

3

Knowing that sec α = 2 and 0< α < /2, calculate the remaining trigonometric ratios of angle α.

4

Knowing that csc α = 3, calculate the remaining trigonometric ratios of angle α.

First quadrant:

 

Second quadrant:

5

Prove the identities:

1

2

3

4

5

6

Simplify the fractions:

1 

 

2 

 

3 

 

7

Prove the identities:

1

 

2

 

8

Simplify the fractions:

1

 

2

 

3

 

9

Calculate the trigonometric ratios of 15º (from the 45º and 30º).

 

10

Develop: cos(x+y+z).

11

Calculate sin 3x, depending on sin x.

 

12

Calculate sin x, cos x and tan x, in terms of tan x/2.