Trigonometry Examples

Convert to Trigonometric Form csc(theta)-sin(theta)
Step 1
Rewrite in terms of sines and cosines.
Step 2
Convert from to .
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 as .
Step 6.2
Apply the product rule to .
Step 6.3
Raise to the power of .
Step 6.4
Multiply by .
Step 6.5
Rewrite in terms of sines and cosines.
Step 6.6
Simplify the expression.
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Step 6.6.1
Apply the product rule to .
Step 6.6.2
One to any power is one.
Step 6.7
Simplify each term.
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Step 6.7.1
Rewrite as .
Step 6.7.2
Rewrite as .
Step 6.7.3
Convert from to .
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 .