Problem

Use the unit-circle diagram to evaluate \(\sin(\pi~/6)\). Give the exact value, its decimal value, and the result rounded to \(\text{four}~\text{decimal}~\text{places}\).

Prompt diagram for M3-034-A14-V01: the target angle and function with the terminal coordinate hidden.

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What this problem is really about

Start with the exact unit-circle coordinate for the requested function, including its quadrant sign. Preserve that fraction or radical before converting to a decimal, and round only the final calculator value to the requested place. A terminating decimal may need trailing zeros to show the stated precision.

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The exact value is sqrt(3)/2; its decimal value is 0.8660254038..., which rounds to 0.8660 to four decimal places.

The exact value is -1/2; its decimal value is -0.5, which rounds to -0.5000 to four decimal places.

The exact value is 1/2; its decimal value is 0.5, which rounds to 0.5001 to four decimal places.

The exact value is 1/2; its decimal value is 0.5, which rounds to 0.5000 to four decimal places.

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Use the unit-circle diagram to evaluate \(\sin(\pi~/6)\). Give the exact value, its decimal value, and the result rounded to \(\text{four}~\text{decimal}~\text{places}\).

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