# sin3x cos3x

## Trigonometry Examples

Solve for x sin(3x)=cos(3x)

Step 1

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Divide each term in the equation by .

Step 3

Cancel the common factor of .

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Step 3.1

Cancel the common factor.

Step 3.2

Step 4

Take the inverse tangent of both sides of the equation lớn extract from inside the tangent.

Step 5

Simplify the right side.

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Step 6

Divide each term in by and simplify.

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Step 6.1

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of .

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Step 6.2.1.1

Cancel the common factor.

Step 6.2.1.2

Step 6.3

Simplify the right side.

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Step 6.3.1

Multiply the numerator by the reciprocal of the denominator.

Step 6.3.2

Multiply .

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Step 7

The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from lớn find the solution in the fourth quadrant.

Step 8

Solve for .

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Step 8.1

Simplify.

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Step 8.1.1

To write as a fraction with a common denominator, multiply by .

Step 8.1.2

Step 8.1.3

Combine the numerators over the common denominator.

Step 8.1.4

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Step 8.2

Divide each term in by and simplify.

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Step 8.2.1

Step 8.2.2

Simplify the left side.

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Step 8.2.2.1

Cancel the common factor of .

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Step 8.2.2.1.1

Cancel the common factor.

Step 8.2.2.1.2

Step 8.2.3

Simplify the right side.

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Step 8.2.3.1

Multiply the numerator by the reciprocal of the denominator.

Step 8.2.3.2

Multiply .

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Step 8.2.3.2.1

Step 8.2.3.2.2

Step 9

Find the period of .

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Step 9.1

The period of the function can be calculated using .

Step 9.2

Replace with in the formula for period.

Step 9.3

The absolute value is the distance between a number and zero. The distance between and is .

Step 10

The period of the function is sánh values will repeat every radians in both directions.

, for any integer

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Step 11