Question

Q 5*
Find the value of sin495​

Answer 1

sin(495) can be written as sin (360° + 135°)

This means that sin completes 1 full rotation which is 360° and comes to an angle of 135°.

So, we can ignore that 360° and write it as:

sin (135°)

= sin (90 + 45)

This is of the form sin (90 + x) which can be simply written as cos x

In other words, sin (90 + x) = cos x

Where x = 45°

So the expression:

sin (90 + 45)

becomes cos 45°

We know the value of cos 45° which is 1/√2

$\therefore \: \boxed{ \bf{sin(495^{ \circ}) = \dfrac{1}{ \sqrt{2} } }}$