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Trigonometry Examples
Step 1
The exact value of is .
Step 2
This is the trigonometric form of a complex number where is the modulus and is the angle created on the complex plane.
Step 3
The modulus of a complex number is the distance from the origin on the complex plane.
where
Step 4
Substitute the actual values of and .
Step 5
Step 5.1
Raising to any positive power yields .
Step 5.2
Apply the product rule to .
Step 5.3
One to any power is one.
Step 5.4
Raise to the power of .
Step 5.5
Add and .
Step 5.6
Rewrite as .
Step 5.7
Any root of is .
Step 5.8
Simplify the denominator.
Step 5.8.1
Rewrite as .
Step 5.8.2
Pull terms out from under the radical, assuming positive real numbers.
Step 6
The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.
Step 7
Since inverse tangent of produces an angle in the first quadrant, the value of the angle is .
Step 8
Substitute the values of and .