Sine, Cosine and Tangent Functions

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What are the Trigonometric Functions?

The three common trigonometry functions are sine, cosine and tangent.

You may use want to use some mnemonics to help you remember the trigonometric functions. One common mnemonic is to remember the SOH-CAH-TOA.

Sine Function

The sine of an angle is the ratio of the opposite side to the hypotenuse side.

Sine is usually abbreviated as sin. Sine * θ* can be written as sin * θ* .

Example:

Calculate the value of sin * θ* in the following triangle.

Solution:

Cosine Function

The cosine of an angle is the ratio of the adjacent side and hypotenuse side.

Cosine is usually abbreviated as cos. Cosine * θ* can be written as cos * θ* .

Example:

Calculate the value of cos * θ* in the following triangle.

Solution:

Tangent Function

The tangent of an angle is the ratio of the opposite side and adjacent side.

Tangent is usually abbreviated as tan. Tangent θ can be written as tan * θ* .

Example:

Calculate the value of tan * θ* in the following triangle.

Solution:

A review of the sine, cosine and tangent functions
How to find a side using trigonometry?

1. Determine which angle you will work with.
2. Name the three sides of the triangle: Hypotenuse, Opposite and Adjacent.
3. The side you know and the side you are looking for determine which ratio you will use: Sine, Cosine or Tangent.

How to find an angle using trigonometry?

1. Determine which angle you will work with.
2. Name the three sides of the triangle: Hypotenuse, Opposite and Adjacent.
3. The side you know and the side you are looking for determine which ratio you will use: Sine, Cosine or Tangent.
4. Set up the ratio.
5. Solve.

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