Question

Sin(701pi/2) find its value

Answer 1

Answer:

answer is 1( after converting it into degrees)sin 90°=1

Answer 2

Answer:

The value of the given sine function is

$\sin( \frac{701\pi}{2} ) = 1$

Explanation:

The given trigonometric relation is

$\sin( \frac{701\pi}{2} )$

This angle might seem very huge to calculate the value of the sine but its very simple if one understands the pattern of trigonometric ratios are multiple angles.

The value of Sin90° is 1

$= > \sin( \frac{\pi}{2} ) = 1$

The value of sin180° is 0

$= > \sin( \frac{2\pi}{2} ) = 0$

The value of sin270° is -1

$= > \sin( \frac{3\pi}{2} ) = - 1$

The value of sin360° is 0

$= > \sin( \frac{4\pi}{2} ) = 0$

From the above values of sine function,we can inteepret that,

$\sin( \frac{n\pi}{2} ) = 0$

If n is even

$\sin( \frac{n\pi}{2} ) = 1$

If n is odd and the angle lies in 1st or 2nd quadrant

$\sin( \frac{n\pi}{2} ) = - 1$

If n is odd and the angle does not lie in 1st and 2nd quadrant.

For our given question,the value of n is 701 which is an odd numbef and the angle lies in between 1st and 2nd quadrant.Therefore,the value is

$\sin( \frac{701\pi}{2} ) = 1$

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