Understanding the Co-Function of Sine and Cosine | A Math Guide for Right Triangles and the Unit Circle

cofunction of sine

The co-function of sine is the function that complements or corresponds to the sine function in a right triangle

The co-function of sine is the function that complements or corresponds to the sine function in a right triangle. The co-function of sine is cosine.

In a right triangle, the sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Mathematically, if θ is an angle, then the sine of θ is denoted as sin(θ) and the cosine of θ is denoted as cos(θ). The co-function identity states that the sine of an angle is equal to the cosine of its complement, and vice versa:

sin(θ) = cos(90° – θ)
cos(θ) = sin(90° – θ)

For example, if we have a right triangle with an angle of 30°, the sine of 30° is equal to the cosine of its complement, which is 60°:

sin(30°) = cos(90° – 30°)
sin(30°) = cos(60°)

This means that if you know the value of the sine of an angle, you can find the value of its complement’s cosine, and vice versa.

The co-function relationship extends beyond right triangles and can be applied to any angle in the unit circle.

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