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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