Question

find the exact value of $sin 60^circ$.
$sin 60^circ = square$
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall the unit circle or special triangle

For a 30-60-90 triangle, the sides are in the ratio \(1:\sqrt{3}:2\). The angle of \(60^{\circ}\) is opposite the side of length \(\sqrt{3}\), and the hypotenuse is of length \(2\).

Step2: Apply the sine definition

The sine of an angle in a right triangle is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\theta = 60^{\circ}\), the opposite side is \(\sqrt{3}\) and the hypotenuse is \(2\). So, \(\sin60^{\circ}=\frac{\sqrt{3}}{2}\).

Answer:

\(\frac{\sqrt{3}}{2}\)