Which expression does the number line represent?
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The exact value of sin 15° is .
Solution:
45 – 30 = 15
sin 15° can be written as sin (45° – 30°).
Using trigonometric difference formula:
sin(A – B) = sin A cos B – cos A sin B
sin (45° – 30°) = sin 45° cos 30° – cos 45° sin 30°
The value of sin 45° =
The value of cos 30° =
The value of cos 45° =
The value of sin 30° =
Substitute these values, we get
Hence the exact value of sin 15° is .