Question

Suppose Sine (x) = negative three-fifths and cos(x) < 0. What the value of cos(2x)?

Answer 1

Answer:

$-\frac{7}{25}$

Step-by-step explanation:

Answer 2

Value of given trigonometric ratio is equals to  $cos (2x) = \frac{7}{25}$.

What is trigonometric ratio?

" Trigonometric ratio is defined as in the right triangle the ratio which represents the relation between sides of a triangle with acute angle of a triangle."

Identity used

$sin^{2} x +cos^{2} x =1\\ \\cos (2x) = cos^{2} x - sin^{2} x$

According to the question,

Given value of trigonometric ratio,

$sin x = \frac{-3}{5} \\\\cosx < 0$

Substitute the value of $sin x$ in the above identity of trigonometric ratio,

$(\frac{-3}{5} )^{2} + cos^{2} x=1\\\\\implies cos^{2}x = 1- \frac{9}{25}\\ \\\implies cos x = \sqrt{\frac{16}{25} } \\\\\implies cos x = \frac{-4}{5} , cos x < 0$

Substitute the value of $sin x$ and $cos x$  the trigonometric identity ,

$cos (2x) =( \frac{-4}{5})^{2} - ( \frac{-3}{5})^{2}\\\\\implies cos (2x) = \frac{16}{25}- \frac{9}{25} \\\\\implies cos (2x) = \frac{7}{25}$

Hence ,  value of given trigonometric ratio is equals to  $cos (2x) = \frac{7}{25}$.

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