Convert to Trigonometric Form sin(x)cos(x)

$\sin (x) \cos (x)$

This is the trigonometric form of a complex number where $| z |$ is the modulus and $θ$ is the angle created on the complex plane.

$z = a + b i = | z | (\cos (θ) + i \sin (θ))$

The modulus of a complex number is the distance from the origin on the complex plane.

$| z | = \sqrt{a^{2} + b^{2}}$ where $z = a + b i$

Substitute the actual values of $a = \sin (x) \cos (x)$ and $b = 0$ .

$| z | = \sqrt{0^{2} + \sin (x) \cos^{2} (x)}$

Find $| z |$ .

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Simplify the expression.

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Raising $0$ to any positive power yields $0$ .

$| z | = \sqrt{0 + \sin (x) \cos^{2} (x)}$

Add $0$ and $\sin (x) \cos^{2} (x)$ .

$| z | = \sqrt{\sin (x) \cos^{2} (x)}$

Reorder $\sin (x)$ and $\cos^{2} (x)$ .

$| z | = \sqrt{\cos^{2} (x) \sin (x)}$

Pull terms out from under the radical.

$| z | = \cos (x) \sqrt{\sin (x)}$

The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.

$θ = \arctan (\frac{0}{\sin (x) \cos (x)})$

Substitute the values of $θ = \arctan (\frac{0}{\sin (x) \cos (x)})$ and $| z | = \cos (x) \sqrt{\sin (x)}$ .

$\cos (x) \sqrt{\sin (x)} (\cos (\arctan (\frac{0}{\sin (x) \cos (x)})) + i \sin (\arctan (\frac{0}{\sin (x) \cos (x)})))$

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Name

Name	sixteen million two hundred seventy-seven thousand nine hundred seventy-eight

Interesting facts

16277978 has 8 divisors, whose sum is 24751668
The reverse of 16277978 is 87977261
Previous prime number is 73

Basic properties

Is Prime? no
Number parity even
Number length 8
Sum of Digits 47
Digital Root 2

Name

Name	one billion two hundred ninety-four million eight hundred sixty-eight thousand

Interesting facts

1294868000 has 256 divisors, whose sum is 12271501944
The reverse of 1294868000 is 0008684921
Previous prime number is 25

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 38
Digital Root 2

Name

Name	nine hundred ninety-five million eighty thousand ninety

Interesting facts

995080090 has 16 divisors, whose sum is 1798835688
The reverse of 995080090 is 090080599
Previous prime number is 233

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 40
Digital Root 4

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