# Trigonometric Identities Problems

### Solutions

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.

## 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.