Trigonometry Examples

Convert to Trigonometric Form sin(theta)+cos(theta)*cot(theta)
Step 1
Simplify each term.
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Step 1.1
Rewrite in terms of sines and cosines.
Step 1.2
Multiply .
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Step 1.2.1
Raise to the power of .
Step 1.2.2
Raise to the power of .
Step 1.2.3
Use the power rule to combine exponents.
Step 1.2.4
Add and .
Step 2
Simplify each term.
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Step 2.1
Factor out of .
Step 2.2
Separate fractions.
Step 2.3
Convert from to .
Step 2.4
Divide by .
Step 3
This is the trigonometric form of a complex number where is the modulus and is the angle created on the complex plane.
Step 4
The modulus of a complex number is the distance from the origin on the complex plane.
where
Step 5
Substitute the actual values of and .
Step 6
Find .
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Step 6.1
Rewrite in terms of sines and cosines.
Step 6.2
Apply the product rule to .
Step 6.3
Multiply .
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Step 6.3.1
Combine and .
Step 6.3.2
Multiply by by adding the exponents.
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Step 6.3.2.1
Multiply by .
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Step 6.3.2.1.1
Raise to the power of .
Step 6.3.2.1.2
Use the power rule to combine exponents.
Step 6.3.2.2
Add and .
Step 6.4
Simplify each term.
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Step 6.4.1
Factor out of .
Step 6.4.2
Multiply by .
Step 6.4.3
Separate fractions.
Step 6.4.4
Convert from to .
Step 6.4.5
Divide by .
Step 7
The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.
Step 8
Substitute the values of and .