# Sine and Cosine Transformation formulas

The sine function can be written as cosine function and vice-versa in trigonometry on the basis of Pythagorean identity of sine and cosine functions.

## Formulas

There are four basic conversion formulas in trigonometry to transform sine function as cosine function and vice-versa.

### Sine to Cosine Transformation

Basically, there are two ways to convert sine function in terms of cosine function.

$(1)\,\,\,\,$ $\sin^2 \theta = 1 -\cos^2 \theta$

The square of sine function can be converted in terms of square of cosine function by this trigonometric formula.

$(2)\,\,\,\,$ $\sin \theta = \pm \sqrt{1 -\cos^2 \theta}$

The sine function can be written in terms of square of cosine function through a square root by this conversion trigonometric identity.

### Cosine to Sine Transformation

Similarly, there are two ways to transform cosine function in terms of sine function.

$(1)\,\,\,\,$ $\cos^2 \theta = 1 -\sin^2 \theta$

The square of cosine function can be transformed in terms of square of sine function by this basic trigonometric identity.

$(2)\,\,\,\,$ $\cos \theta = \pm \sqrt{1 -\sin^2 \theta}$

The cosine function can be expressed in terms of square of sine function through a square root by this transformation trigonometric identity.

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