Convert to Trigonometric Form 2sin(10 degrees )cos(10 degrees )

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Trigonometry

$2 \sin (10 °) \cos (10 °)$

Apply the sine double-angle identity.

$\sin (2 \cdot 10 °)$

Multiply $2$ by $10 °$ .

$\sin (20)$

Evaluate $\sin (20)$ .

$0.34202014$

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 $a = 0.34202014$ and $b = 0$ .

$| z | = \sqrt{0^{2} + {0.34202014}^{2}}$

Find $| z |$ .

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

$| z | = \sqrt{0 + {0.34202014}^{2}}$

Raise $0.34202014$ to the power of $2$ .

$| z | = \sqrt{0 + 0.11697777}$

Add $0$ and $0.11697777$ .

$| z | = \sqrt{0.11697777}$

Evaluate the root.

$| z | = 0.34202014$

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

$θ = \arctan (\frac{0}{0.34202014})$

Since inverse tangent of $\frac{0}{0.34202014}$ produces an angle in the first quadrant, the value of the angle is $0$ .

$θ = 0$

Substitute the values of $θ = 0$ and $| z | = 0.34202014$ .

$0.34202014 (\cos (0) + i \sin (0))$

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Name

Name	one billion five hundred sixty-nine million five hundred twenty-eight thousand ninety

Interesting facts

1569528090 has 32 divisors, whose sum is 2879723280
The reverse of 1569528090 is 0908259651
Previous prime number is 13

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 45
Digital Root 9

Name

Name	one billion three hundred eight million four hundred seventy-one thousand six hundred six

Interesting facts

1308471606 has 64 divisors, whose sum is 2872074240
The reverse of 1308471606 is 6061748031
Previous prime number is 97

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 36
Digital Root 9

Name

Name	two hundred forty million sixty-six thousand two hundred sixty-five

Interesting facts

240066265 has 8 divisors, whose sum is 288325440
The reverse of 240066265 is 562660042
Previous prime number is 1207

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 31
Digital Root 4

Find the Other Trig Values in Quadrant III sin(x)=-11/61

Graph y=1/4*sec(x)

Solve for ? cos(theta)=( square root of 2)/2

Graph y=4csc(4x)

Solve for ? sin(x/2)=1/2