Trigonometry Examples

$\sin (\frac{4}{9} + \frac{π}{6})$

Step 1

Use the sum formula for sine to simplify the expression. The formula states that $\sin (A + B) = \sin (A) \cos (B) + \cos (A) \sin (B)$ .

$\sin (\frac{4}{9}) \cos (\frac{π}{6}) + \cos (\frac{4}{9}) \sin (\frac{π}{6})$

Step 2

Remove parentheses.

$\sin (\frac{4}{9}) \cos (\frac{π}{6}) + \cos (\frac{4}{9}) \sin (\frac{π}{6})$

Step 3

Simplify each term.

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Step 3.1

Evaluate $\sin (\frac{4}{9})$ .

$0.42995636 \cos (\frac{π}{6}) + \cos (\frac{4}{9}) \sin (\frac{π}{6})$

Step 3.2

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$0.42995636 \frac{\sqrt{3}}{2} + \cos (\frac{4}{9}) \sin (\frac{π}{6})$

Step 3.3

Multiply $0.42995636 \frac{\sqrt{3}}{2}$ .

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Step 3.3.1

Combine $0.42995636$ and $\frac{\sqrt{3}}{2}$ .

$\frac{0.42995636 \sqrt{3}}{2} + \cos (\frac{4}{9}) \sin (\frac{π}{6})$

Step 3.3.2

Multiply $0.42995636$ by $\sqrt{3}$ .

$\frac{0.74470626}{2} + \cos (\frac{4}{9}) \sin (\frac{π}{6})$

Step 3.4

Divide $0.74470626$ by $2$ .

$0.37235313 + \cos (\frac{4}{9}) \sin (\frac{π}{6})$

Step 3.5

Evaluate $\cos (\frac{4}{9})$ .

$0.37235313 + 0.90284966 \sin (\frac{π}{6})$

Step 3.6

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$0.37235313 + 0.90284966 (\frac{1}{2})$

Step 3.7

Combine $0.90284966$ and $\frac{1}{2}$ .

$0.37235313 + \frac{0.90284966}{2}$

Step 3.8

Divide $0.90284966$ by $2$ .

$0.37235313 + 0.45142483$

Step 4

Add $0.37235313$ and $0.45142483$ .

$0.82377796$