Trigonometry Examples

$\frac{6}{7} \cdot (\cos (111) i) + \frac{6}{7} \cdot (\sin (111) j)$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{6}{7} (\cos (111) i)$ .

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Step 1.1.1

Combine $\cos (111)$ and $\frac{6}{7}$ .

$\frac{\cos (111) \cdot 6}{7} i + \frac{6}{7} \cdot (\sin (111) j)$

Step 1.1.2

Combine $\frac{\cos (111) \cdot 6}{7}$ and $i$ .

$\frac{\cos (111) \cdot 6 i}{7} + \frac{6}{7} \cdot (\sin (111) j)$

Step 1.2

Move $6$ to the left of $\cos (111)$ .

$\frac{6 \cos (111) i}{7} + \frac{6}{7} \cdot (\sin (111) j)$

Step 1.3

Multiply $\frac{6}{7} (\sin (111) j)$ .

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Step 1.3.1

Combine $\sin (111)$ and $\frac{6}{7}$ .

$\frac{6 \cos (111) i}{7} + \frac{\sin (111) \cdot 6}{7} j$

Step 1.3.2

Combine $\frac{\sin (111) \cdot 6}{7}$ and $j$ .

$\frac{6 \cos (111) i}{7} + \frac{\sin (111) \cdot 6 j}{7}$

Step 1.4

Move $6$ to the left of $\sin (111)$ .

$\frac{6 \cos (111) i}{7} + \frac{6 \sin (111) j}{7}$

Step 2

Reorder factors in $\frac{6 \cos (111) i}{7} + \frac{6 \sin (111) j}{7}$ .

$\frac{6 i \cos (111)}{7} + \frac{6 j \sin (111)}{7}$