Question

What are the coordinates for the angle π/4 on tge unit circle

Answer 1

Answer: Both x and y are $\frac{\sqrt{2}}{2}$ which is the same as $\frac{1}{\sqrt{2}}$

In other words, the point $\left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$ is on the unit circle for the angle pi/4 radians. This point is equivalent to $\left( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$

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Explanation:

The angle pi/4 radians is equivalent to 45 degrees. Draw out a 45-45-90 triangle with hypotenuse 1, and you'll find the congruent legs are each $\frac{1}{\sqrt{2}}$ units long (apply the pythagorean theorem). If you apply the sine and cosine ratios, you'll get the answer shown above.

Recall that

• x = cos(theta)
• y = sin(theta)

and also

• cos = adjacent/hypotenuse
• sin = opposite/hypotenuse

The pythagorean theorem is a^2+b^2 = c^2.