Precalculus Examples

Find the Exact Value sin(arccos(3/7))
Step 1
Draw a triangle in the plane with vertices , , and the origin. Then is the angle between the positive x-axis and the ray beginning at the origin and passing through . Therefore, is .
Step 2
Rewrite as .
Step 3
Simplify the numerator.
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Step 3.1
Rewrite as .
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Step 3.1.1
Factor out of .
Step 3.1.2
Rewrite as .
Step 3.2
Pull terms out from under the radical.
Step 4
Simplify the denominator.
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Step 4.1
Rewrite as .
Step 4.2
Pull terms out from under the radical, assuming positive real numbers.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: