determine the exact value of sin(π/6)
determine the exact value of sin(π/6)
Answer
Explanation:
Step1: Recall the unit - circle values
On the unit circle, for an angle (\theta=\frac{\pi}{6}) (or (30^{\circ})), we can use the right - triangle definitions. In a (30 - 60-90) triangle, if the hypotenuse (r = 1) (unit - circle radius), the opposite side (y) (where (\sin\theta=\frac{y}{r})) has length (y=\frac{1}{2}) when (r = 1).
Step2: Apply the sine formula
The formula for sine is (\sin\theta=\frac{y}{r}). Since (r = 1) (unit circle) and (y=\frac{1}{2}) for (\theta=\frac{\pi}{6}), we have (\sin\left(\frac{\pi}{6}\right)=\frac{\frac{1}{2}}{1}).
Answer:
(\frac{1}{2})