What are the sine, cosine, and tangent of θ = 3 pi over 4 radians?

Solution:

Given, θ = 3 pi over 4 radians

We have to find the sine, cosine and tangent.

Consider a unit circle.

First find the reference angle.

The given angle θ = 3 pi over 4 radians lies in the second quadrant because it is less than 𝜋.

Second quadrant means the reference angle = 𝜋 - 3𝜋/4  = 𝜋/4

Now, Sine theta will be opposite / hypotenuse

\(sin(\frac{3\pi }{4})=\frac{1}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}\)

Cosine theta will be adjacent / hypotenuse

\(cos(\frac{3\pi }{4})=\frac{-1}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}=\frac{-\sqrt{2}}{2}\)

Tangent will be opposite / adjacent

\(tan(\frac{3\pi }{4})=\frac{1}{-1}=-1\)

Therefore, the sine, cosine and tangent of θ = 3 pi over 4 radians are \(\frac{\sqrt{2}}{2},\frac{-\sqrt{2}}{2}\, and\, -1\).

---

What are the sine, cosine, and tangent of θ = 3 pi over 4 radians?

Summary:

The sine, cosine and tangent of θ = 3 pi over 4 radians are \(\frac{\sqrt{2}}{2},\frac{-\sqrt{2}}{2}\, and\, -1\).