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Trigonometry Examples
Step 1
If , then .
Step 2
Step 2.1
Apply the sum of angles identity .
Step 2.2
Simplify each term.
Step 2.2.1
The functions cosine and arccosine are inverses.
Step 2.2.2
The functions cosine and arccosine are inverses.
Step 2.2.3
Rewrite using the commutative property of multiplication.
Step 2.2.4
Multiply by by adding the exponents.
Step 2.2.4.1
Move .
Step 2.2.4.2
Multiply by .
Step 2.2.5
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 2.2.6
Rewrite as .
Step 2.2.7
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 2.2.8
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 2.2.9
Rewrite as .
Step 2.2.10
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 2.2.11
Multiply by .
Step 2.2.12
Combine using the product rule for radicals.
Step 3
Step 3.1
The exact value of is .
Step 4
Step 4.1
Graph each side of the equation. The solution is the x-value of the point of intersection.
Step 5
Exclude the solutions that do not make true.
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: