Find the Value of sin(5pi/2) | Sin 5π/2 Value

The value of sin(5pi/2) is equal to 1. The angle 5π/2 is equivalent to 450° and the value of sin 450° is equal to 1. The sin 5π/2 formula is given by

$\sin {\displaystyle \frac{5\pi }{2}}=1.$

Let us learn how to find the value of sin(5pi/2).

Value of Sin(5π/2)

Answer: The value of sin 5π/2 is 1.

Explanation:

By using the formula sin(a+b) =sina cosb +cosa sinb, the value of sin(5π/2) will be equal to

$\sin {\displaystyle \frac{5\pi }{2}}$ $=\sin (2\pi +{\displaystyle \frac{\pi }{2}})$

= $\sin 2\pi \cos {\displaystyle \frac{\pi }{2}}+\cos 2\pi \sin {\displaystyle \frac{\pi }{2}}$

= 0 ⋅ 1 + (-1)²⋅1 as we know sin nπ =0, cos nπ =(-1)ⁿ, sin(π/2)=1, cos(π/2)=0.

= 0+1

= 1.

So the value of sin(5π/2) is equal to 1.

Also Read: Sin(π-x) Formula | Value of sin(3π/2)

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Value of Sin(-5pi/2)

By using the rule sin(-θ) = -sinθ, the value of sine of negative 5pi/2 will be equal to

sin(-5π/2) = -sin(5π/2) = -1, by the above.

∴ sin(-5π/2) = -1.

Thus, the value of sin(-5π/2) is equal to -1.

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