The cosine angle can be found by converting it in terms of acute angle and further simplify.
What is cosine angle?
The cosine of an angle is defined as the sine of the complementary angle. In a right-triangle, cosine is defined as the ratio of the length of the adjacent side to that of the longest side i.e. the hypotenuse.
For the given situation,
cos(315°) = √2/2
We can put cos(315°) in terms of 360°
⇒ [tex]cos(315)=cos (360-315)[/tex]
⇒ [tex]cos(315)=cos(45)[/tex]
we know that
⇒ [tex]cos(45)=\frac{1}{\sqrt{2} }[/tex]
⇒ [tex]cos(315)=(\frac{1 }{\sqrt{2} } ) (\frac{\sqrt{2} }{\sqrt{2} } )[/tex]
⇒ [tex]cos(315)=\frac{\sqrt{2} }{2}[/tex]
Cosine is positive in 4th quadrant, so the value of cosine is positive.
Hence we can conclude that the cosine angle can be found by converting it in terms of acute angle and further simplify.
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