PS: Note that all the angles are in degree.

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Exercise 1

Knowing that $\text{[math]}$ , and that $\text{[math]}$ , calculate the remaining trigonometric ratios of angle $\text{[math]}$ .

Exercise 2

Knowing that $\text{[math]}$ , and that $\text{[math]}$ , calculate the remaining trigonometric ratios of angle $\text{[math]}$ .

Exercise 3

Knowing that $\text{[math]}$ and $\text{[math]}$ , calculate the remaining trigonometric ratios of angle $\text{[math]}$ .

Exercise 4

Knowing that $\text{[math]}$ , calculate the remaining trigonometric ratios of angle $\text{[math]}$ .

Exercise 5

Prove the identities:

1 $\text{[math]}$

2 $\text{[math]}$

3 $\text{[math]}$

4 $\text{[math]}$

5 $\text{[math]}$

Exercise 6

Simplify the fractions:

1 $\text{[math]}$

2 $\text{[math]}$

3 $\text{[math]}$

Exercise 7

Prove the identities:

Part 1

$\text{[math]}$

Part 2

$\text{[math]}$

Exercise 8

Simplify the fractions:

Part 1

$\text{[math]}$

Part 2

$\text{[math]}$

Part 3

$\text{[math]}$

Exercise 9

Calculate the trigonometric ratios of $\text{[math]}$ (from the $\text{[math]}$ and $\text{[math]}$ ).

Exercise 10

Develop: $\text{[math]}$ .

Exercise 11

Calculate $\text{[math]}$ , depending on $\text{[math]}$ .

Exercise 12

Calculate $\text{[math]}$ and $\text{[math]}$ , in terms of $\text{[math]}$ .

Solution of exercise 1

Knowing that $\text{[math]}$ , and that $\text{[math]}$ , calculate the remaining trigonometric ratios of angle $\text{[math]}$ .

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 2

Knowing that $\text{[math]}$ , and that $\text{[math]}$ , calculate the remaining trigonometric ratios of angle $\text{[math]}$ .

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 3

Knowing that $\text{[math]}$ and $\text{[math]}$ , calculate the remaining trigonometric ratios of angle $\text{[math]}$ .

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 4

Knowing that $\text{[math]}$ , calculate the remaining trigonometric ratios of angle $\text{[math]}$ .

First quadrant:

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Second quadrant:

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 5

Prove the identities:

1 $\text{[math]}$

$\text{[math]}$ $\text{[math]}$

2 $\text{[math]}$

$\text{[math]}$

3 $\text{[math]}$

$\text{[math]}$

4 $\text{[math]}$

$\text{[math]}$

5 $\text{[math]}$

$\text{[math]}$

Solution of exercise 6

Simplify the fractions:

1 $\text{[math]}$

$\text{[math]}$

2 $\text{[math]}$

$\text{[math]}$ $\text{[math]}$

3 $\text{[math]}$

$\text{[math]}$ $\text{[math]}$

Solution of exercise

Solution of exercise 7

Prove the identities:

1 $\text{[math]}$

$\text{[math]}$

2 $\text{[math]}$

$\text{[math]}$ $\text{[math]}$

Solution of exercise

Solution of exercise 8

Simplify the fractions:

1 $\text{[math]}$

$\text{[math]}$

2 $\text{[math]}$

$\text{[math]}$

3 $\text{[math]}$

$\text{[math]}$

Solution of exercise

Solution of exercise 9

Calculate the trigonometric ratios of $\text{[math]}$ (from the $\text{[math]}$ and $\text{[math]}$ ).

$\text{[math]}$

Solution of exercise

Solution of exercise 10

Develop: $\text{[math]}$ .

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 11

Calculate $\text{[math]}$ , depending on $\text{[math]}$ .

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 12

Calculate $\text{[math]}$ and $\text{[math]}$ , in terms of $\text{[math]}$ .

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$

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Trigonometric Identities Problems

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Part 1

Part 2

Exercise 8

Part 1

Part 2

Part 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

Theory

Trigonometric Values

Trigonometric Identities

Trigonometric Ratios

Trigonometric Formulas

Systems of Simultaneous Trigonometric Equations

Unit Circle

Sine and Cosine Law

Solving Right Triangles

Even-Odd Identities

Oblique Triangles

Pythagorean Identities

Measurement of Angles

Other Trigonometric Identities

Trigonometric Equations

Cofunction Identities

Exercises

Trigonometric Identities Problems

Oblique Triangle Word Problems

Trigonometric Angles Worksheet

Right Triangle Word Problems

Trigonometric Equations Worksheet

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