Math Doubts

Sine to Cosine Transformation formulas

Sine and Cosine functions are different trigonometric functions. It is not possible to express sine in terms of cosine directly but Pythagorean identity for sine and cosine is made it possible.

According to Pythagorean identity of sine and cosine functions, the sum of the squares of sine and cosine functions is one.

$\sin^2{\theta}+\cos^2{\theta} = 1$

On the basis of this trigonometric identity, sine function can be converted as cosine function in two forms.

Transforming square of sine function

Shift square of cosine function to right hand side of the Pythagorean identity to get square of sine function in terms of square of cosine function.

$\sin^2{\theta} = 1-\cos^2{\theta}$

It is used as a formula to replace square of sine function in terms of cosine function in mathematics.

Transforming sine function

Take square root both sides to express sine function in terms of square of cosine function through a square root.

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

Thus, a sine function can be transformed in terms of cosine function in two different ways possibly.

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