Trigonometric Functions / Trigonometric Ratios

In this lesson, we will look at the three basic trigonometric functions (trigonometric ratios): Tangent, Sine and Cosine

Trigonometric Functions: Tangent of an Angle

We first consider the 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 .

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

Example:

Calculate the value of tan θ in the following triangle.

Solution:

Trigonometric Functions: Sine of an Angle

Next. we consider the 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:

Trigonometric Functions: Cosine of an Angle

Next, we consider the 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:

Videos

Have a look at the following video for more examples:

Find the trigonometric ratios for the right triangle.

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Trigonometry