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Step 1:I'll solve this step-by-step using precise LaTeX formatting:
Step 2:: Recall the special angle values for sine
The sine of 60° is a well-known trigonometric value that can be derived from the unit circle or special right triangles.
Step 3:: Visualize the 30 - 60 - 90 triangle
In a 30-60-90 triangle, the side lengths are proportional to $$1 : \sqrt{3} : 2$$.
At the 60° angle, the sine represents the length of the opposite side divided by the hypotenuse.
Step 4:: Calculate the sine value
- $$\frac{\sqrt{3}}{2}$$ is the simplified fraction representing this ratio
This is because: - The hypotenuse has length 2
Final Answer
\sin(60°) = \frac{\sqrt{3}}{2} \approx 0.866
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