Question

find the exact value of sin 30°.

sin 30° =
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall special triangle values

In a 30 - 60 - 90 right - triangle, the side opposite the \(30^{\circ}\) angle is half the hypotenuse. Let the hypotenuse length be \(c = 2\) and the side opposite the \(30^{\circ}\) angle be \(a = 1\).
The sine of an angle in a right - triangle is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Apply the sine formula for \(30^{\circ}\)

For \(\theta = 30^{\circ}\), \(\sin30^{\circ}=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the side opposite \(30^{\circ}\) is \(1\) and the hypotenuse is \(2\). So \(\sin30^{\circ}=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)