Question

what is sin 45°?

a. √2
b. 1/2
c. 1
d. 1/√2

Explanation:

Step1: Recall sine function definition

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).
For \(\theta = 45^{\circ}\), the opposite side length is \(1\) and the hypotenuse length is \(\sqrt{2}\).
So, \(\sin45^{\circ}=\frac{1}{\sqrt{2}}\).
We can rationalize \(\frac{1}{\sqrt{2}}\) by multiplying numerator and denominator by \(\sqrt{2}\), \(\frac{1\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{\sqrt{2}}{2}\), but \(\frac{1}{\sqrt{2}}\) is also a valid form.

Answer:

D. \(\frac{1}{\sqrt{2}}\)