Trigonometry Examples

$y = \frac{5}{2} \cdot \cos (x + \frac{2 π}{3})$

Step 1

Rewrite the equation as $\frac{5}{2} \cdot \cos (x + \frac{2 π}{3}) = y$ .

$\frac{5}{2} \cdot \cos (x + \frac{2 π}{3}) = y$

Step 2

Multiply both sides of the equation by $\frac{2}{5}$ .

$\frac{2}{5} (\frac{5}{2} \cos (x + \frac{2 π}{3})) = \frac{2}{5} y$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $\frac{2}{5} (\frac{5}{2} \cos (x + \frac{2 π}{3}))$ .

Tap for more steps...

Step 3.1.1.1

Combine $\frac{5}{2}$ and $\cos (x + \frac{2 π}{3})$ .

$\frac{2}{5} \cdot \frac{5 \cos (x + \frac{2 π}{3})}{2} = \frac{2}{5} y$

Step 3.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.1.2.1

Cancel the common factor.

$\frac{2}{5} \cdot \frac{5 \cos (x + \frac{2 π}{3})}{2} = \frac{2}{5} y$

Step 3.1.1.2.2

Rewrite the expression.

$\frac{1}{5} (5 \cos (x + \frac{2 π}{3})) = \frac{2}{5} y$

Step 3.1.1.3

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.1.1.3.1

Factor $5$ out of $5 \cos (x + \frac{2 π}{3})$ .

$\frac{1}{5} (5 \cos (x + \frac{2 π}{3})) = \frac{2}{5} y$

Step 3.1.1.3.2

Cancel the common factor.

$\frac{1}{5} (5 \cos (x + \frac{2 π}{3})) = \frac{2}{5} y$

Step 3.1.1.3.3

Rewrite the expression.

$\cos (x + \frac{2 π}{3}) = \frac{2}{5} y$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Combine $\frac{2}{5}$ and $y$ .

$\cos (x + \frac{2 π}{3}) = \frac{2 y}{5}$

Step 4

Take the inverse cosine of both sides of the equation to extract $x$ from inside the cosine.

$x + \frac{2 π}{3} = \arccos (\frac{2 y}{5})$

Step 5

Subtract $\frac{2 π}{3}$ from both sides of the equation.

$x = \arccos (\frac{2 y}{5}) - \frac{2 π}{3}$