Trigonometry Examples

$z_{1} = 6 (\cos (20 °) + i \sin (20 °))$

Step 1

Simplify $6 (\cos (20 °) + i \sin (20 °))$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Evaluate $\cos (20 °)$ .

$z_{1} = 6 (0.93969262 + i \sin (20 °))$

Step 1.1.2

Evaluate $\sin (20 °)$ .

$z_{1} = 6 (0.93969262 + i \cdot 0.34202014)$

Step 1.1.3

Move $0.34202014$ to the left of $i$ .

$z_{1} = 6 (0.93969262 + 0.34202014 i)$

$z_{1} = 6 (0.93969262 + 0.34202014 i)$

Step 1.2

Simplify by multiplying through.

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Step 1.2.1

Apply the distributive property.

$z_{1} = 6 \cdot 0.93969262 + 6 (0.34202014 i)$

Step 1.2.2

Multiply.

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Step 1.2.2.1

Multiply $6$ by $0.93969262$ .

$z_{1} = 5.63815572 + 6 (0.34202014 i)$

Step 1.2.2.2

Multiply $0.34202014$ by $6$ .

$z_{1} = 5.63815572 + 2.05212085 i$

$z_{1} = 5.63815572 + 2.05212085 i$

$z_{1} = 5.63815572 + 2.05212085 i$

$z_{1} = 5.63815572 + 2.05212085 i$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$