Math Doubts

Cosine to Sine Transformation formulas

Cosine and sine functions are distinct functions. So, it is not possible to write cosine function in terms of sine function but the Pythagorean identity for cosine and sine is made it easier.

As per Pythagorean identity of sine and cosine functions, the sum of the squares of cosine and sine functions is equal to one.

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

Cosine function can be converted in terms of sine function in the following forms on this basis of this Pythagorean trigonometric identity.

Transforming square of Cosine function

Move square of sine function to right hand side of the Pythagorean identity for obtaining square of cosine function in terms of square of sine function.

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

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

Transforming Cosine function

Take square root both sides of the equation to write cosine function in terms of square of sine function through a square root.

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

In this way, a cosine function can be converted as the sine function in these two possible ways.



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