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## Formulas for the Trigonometric Identities

Trigonometric identities are useful when we want to rewrite or simplify trigonometric expressions. Trigonometric identities are true for every value that occurs on both sides of an equation. All trigonometric identities are derived from the six fundamental...

## Quotient Identities – Formulas and Examples

Quotient identities are trigonometric identities that are written as fractions of the sine and cosine functions. The tangent forms a quotient identity and can be written as the sine of the angle divided by the cosine. Similarly, the cotangent can be written as the...

## Reciprocal Identities – Formulas and examples

We have already become familiar with the trigonometric functions of sine, cosine, and tangent. These functions are written as fractions relating to the sides of a right triangle. We also know that the reciprocal of a fraction is equal to the original fraction with its...

## Pythagorean Identities – Formulas, Proof and Examples

Pythagorean identities are identities in trigonometry that are extensions of the Pythagorean theorem. Pythagorean identities are useful for simplifying trigonometric expressions. These identities are especially used to write expressions such as a sine or cosine...

## Law of Sines and Cosines – Formulas and Examples

The laws of sine and cosine are relations that allow us to find the length of one side of a triangle or the measure of one of its angles. Depending on the information we have available, we can use the law of sines or the law of cosines. The law of sines relates the...

## Law of Cosines – Examples and Practice Problems

The law of cosines is an equation that relates the lengths of two sides of a triangle and their intermediate angle. We can apply the law of cosines when we want to find the length of the third side of a triangle and we know the other two sides and their intermediate...