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 < pi/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:

1Trigonometric Identity Exercise

2Trigonometric Identity Exercise

3Trigonometric Identity Exercise

4Trigonometric Identity Exercise

5Trigonometric Identity Exercise

6 Simplify the fractions:

1 Trigonometric Exercise

2 Trigonometric Exercise

3 Trigonometric Exercise

7Prove the identities:

1Trigonometric Exercise

2Trigonometric Exercise

8Simplify the fractions:

1Trigonometric Exercise

2Trigonometric Exercise

3Trigonometric Exercise

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.

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution


2

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

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution


3

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

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution


4

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

First quadrant:

solución

Trigonometric Operations

Trigonometric Solution

 

Second quadrant:

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution


5

Prove the identities:

1Trigonometric Exercise

Trigonometric Operations

Trigonometric Solution


2Trigonometric Exercise

Trigonometric Operations

Trigonometric Solution


3Trigonometric Exercise

Trigonometric Solution


4Trigonometric Exercise

Trigonometric Solution


5Trigonometric Exercise

Trigonometric Solution



6

Simplify the fractions:

1 Trigonometric Exercise

Trigonometric Solution

 

2 Trigonometric Exercise

Trigonometric Operations

Trigonometric Solution

 

3 Trigonometric Exercise

Trigonometric Operations

Trigonometric Solution


 

7

Prove the identities:

1Trigonometric Exercise

Trigonometric Solution

 

2Trigonometric Exercise

Trigonometric Operations

Trigonometric Solution


 

8

Simplify the fractions:

1Trigonometric Exercise

Trigonometric Solution

 

2Trigonometric Exercise

Trigonometric Solution

 

3Trigonometric Exercise

Trigonometric Solution


 

9

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

razones

Trigonometric Solution

razones

Trigonometric Solution


 

10

Develop: cos(x+y+z).

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution


11

Calculate sin 3x, depending on sin x.

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution

 

12

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

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution

 



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