Find Value of sin(3pi/4) | Sin 3π/4 Value

The value of sin(3pi/4) is equal to 1/√2. As the angle 3π/4 is same as 135° in degrees, the value of sin135° is 1/√2.

The sin 3π/4 formula is given as follows

$\boxed{\sin \dfrac{3\pi}{4}=\dfrac{1}{\sqrt{2}} }$

Let us learn how to find the value of sin(3pi/4).

Value of Sin(3π/4)

Answer: The value of sin 3π/4 is equal to 1/√2.

Explanation:

Note that

$\dfrac{3\pi}{4}=\dfrac{\pi}{2}+\dfrac{\pi}{4}$.

Using the formula sin(a+b) =sina cosb +cosa sinb with a=π/2 and b=π/4, the value of sin(3π/4) is given by

$\sin \dfrac{3\pi}{4}$ $=\sin \big(\dfrac{\pi}{2}+\dfrac{\pi}{4} \big)$

= $\sin \dfrac{\pi}{2} \cos \dfrac{\pi}{4} + \cos \dfrac{\pi}{2} \sin \dfrac{\pi}{4}$

= $1 \cdot \dfrac{1}{\sqrt{2}} + 0 \cdot \dfrac{1}{\sqrt{2}}$ as we know sinπ/2 =1, cos π/2 =0, sin(π/4)=cos(π/4)=1/√2.

= 1/√2+0

= 1/√2.

So the value of sin(3pi/4) is equal to 1/√2.

Also Read: Simplify cos³x -sin³x

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Value of Sin(-3pi/4)

As sin(-θ) = -sinθ, the value of sine of negative 3pi/4 is given by

sin(-3π/4) = -sin(3π/4) = -1/√2.

∴ sin(-3π/4) = -1/√2.

Thus, the value of sin(-3π/4) is equal to -1/√2.

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