Chapters

- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 1
- Exercise 2
- Exercise 8
- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 9
- Exercise 10
- Exercise 11
- Exercise 12
- Solution of exercise 1
- Solution of exercise 2
- Solution of exercise 3
- Solution of exercise 4
- Solution of exercise 5
- Solution of exercise 6
- Solution of exercise
- Solution of exercise 7
- Solution of exercise
- Solution of exercise 8
- Solution of exercise
- Solution of exercise 9
- Solution of exercise
- Solution of exercise 10
- Solution of exercise 11
- Solution of exercise 12

## Exercise 1

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

## Exercise 2

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

## Exercise 3

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

## Exercise 4

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

## Exercise 5

Prove the identities:

1

2

3

4

5

## Exercise 6

Simplify the fractions:

1

2

3

## Exercise 7

Prove the identities:

## Exercise 1

## Exercise 2

## Exercise 8

Simplify the fractions:

## Exercise 1

## Exercise 2

## Exercise 3

## Exercise 9

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

## Exercise 10

Develop: cos(x+y+z).

## Exercise 11

Calculate sin 3x, depending on sin x.

## Exercise 12

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

## Solution of exercise 1

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

## Solution of exercise 2

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

## Solution of exercise 3

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

## Solution of exercise 4

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

First quadrant:

Second quadrant:

## Solution of exercise 5

Prove the identities:

1

2

3

4

5

## Solution of exercise 6

Simplify the fractions:

1

2

3

## Solution of exercise

## Solution of exercise 7

Prove the identities:

1

2

## Solution of exercise

## Solution of exercise 8

Simplify the fractions:

1

2

3

## Solution of exercise

## Solution of exercise 9

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

## Solution of exercise

## Solution of exercise 10

Develop: cos(x+y+z).

## Solution of exercise 11

Calculate sin 3x, depending on sin x.

## Solution of exercise 12

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

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