Question

find the exact value of sin 60°

sin 60° =
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall the unit circle or special triangles

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

Step2: Apply the sine formula

Using the definition \(\sin 60^\circ=\frac{\text{opposite}}{\text{hypotenuse}}\), we substitute the values from the 30 - 60 - 90 triangle. So \(\sin 60^\circ=\frac{\sqrt{3}}{2}\).

Answer:

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