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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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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