## 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.      ## 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 7

Prove the identities:

1  2   ## Solution of exercise 8

Simplify the fractions:

1  2  3  ## Solution of exercise 9

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