Trigonometry Examples

$x \cdot \cos (150) + y \cdot \cos (45) = x \cdot \sin (30) + y \cdot \sin (45) - 700$

Step 1

Solve for $y$ .

Tap for more steps...

Step 1.1

Move all terms containing $y$ to the left side of the equation.

Tap for more steps...

Step 1.1.1

Subtract $\frac{y \sqrt{2}}{2}$ from both sides of the equation.

$- \frac{x \sqrt{3}}{2} + \frac{y \sqrt{2}}{2} - \frac{y \sqrt{2}}{2} = \frac{x}{2} - 700$

Step 1.1.2

Combine the opposite terms in $- \frac{x \sqrt{3}}{2} + \frac{y \sqrt{2}}{2} - \frac{y \sqrt{2}}{2}$ .

Tap for more steps...

Step 1.1.2.1

Subtract $\frac{y \sqrt{2}}{2}$ from $\frac{y \sqrt{2}}{2}$ .

$- \frac{x \sqrt{3}}{2} + 0 = \frac{x}{2} - 700$

Step 1.1.2.2

Add $- \frac{x \sqrt{3}}{2}$ and $0$ .

$- \frac{x \sqrt{3}}{2} = \frac{x}{2} - 700$

Step 1.2

Multiply both sides by $2$ .

$- \frac{x \sqrt{3}}{2} \cdot 2 = (\frac{x}{2} - 700) \cdot 2$

Step 1.3

Simplify.

Tap for more steps...

Step 1.3.1

Simplify the left side.

Tap for more steps...

Step 1.3.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.3.1.1.1

Move the leading negative in $- \frac{x \sqrt{3}}{2}$ into the numerator.

$\frac{- x \sqrt{3}}{2} \cdot 2 = (\frac{x}{2} - 700) \cdot 2$

Step 1.3.1.1.2

Cancel the common factor.

$\frac{- x \sqrt{3}}{2} \cdot 2 = (\frac{x}{2} - 700) \cdot 2$

Step 1.3.1.1.3

Rewrite the expression.

$- x \sqrt{3} = (\frac{x}{2} - 700) \cdot 2$

Step 1.3.2

Simplify the right side.

Tap for more steps...

Step 1.3.2.1

Simplify $(\frac{x}{2} - 700) \cdot 2$ .

Tap for more steps...

Step 1.3.2.1.1

Apply the distributive property.

$- x \sqrt{3} = \frac{x}{2} \cdot 2 - 700 \cdot 2$

Step 1.3.2.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.3.2.1.2.1

Cancel the common factor.

$- x \sqrt{3} = \frac{x}{2} \cdot 2 - 700 \cdot 2$

Step 1.3.2.1.2.2

Rewrite the expression.

$- x \sqrt{3} = x - 700 \cdot 2$

Step 1.3.2.1.3

Multiply $- 700$ by $2$ .

$- x \sqrt{3} = x - 1400$

Step 1.4

Solve for $x$ .

Tap for more steps...

Step 1.4.1

Subtract $x$ from both sides of the equation.

$- x \sqrt{3} - x = - 1400$

Step 1.4.2

Factor $- x$ out of $- x \sqrt{3} - x$ .

Tap for more steps...

Step 1.4.2.1

Factor $- x$ out of $- x \sqrt{3}$ .

$- x \sqrt{3} - x = - 1400$

Step 1.4.2.2

Factor $- x$ out of $- x$ .

$- x \sqrt{3} - x \cdot 1 = - 1400$

Step 1.4.2.3

Factor $- x$ out of $- x (\sqrt{3}) - x (1)$ .

$- x (\sqrt{3} + 1) = - 1400$

Step 1.4.3

Divide each term in $- x (\sqrt{3} + 1) = - 1400$ by $- \sqrt{3} - 1$ and simplify.

Tap for more steps...

Step 1.4.3.1

Divide each term in $- x (\sqrt{3} + 1) = - 1400$ by $- \sqrt{3} - 1$ .

$\frac{- x (\sqrt{3} + 1)}{- \sqrt{3} - 1} = \frac{- 1400}{- \sqrt{3} - 1}$

Step 1.4.3.2

Simplify the left side.

Tap for more steps...

Step 1.4.3.2.1

Cancel the common factor of $\sqrt{3} + 1$ and $- \sqrt{3} - 1$ .

Tap for more steps...

Step 1.4.3.2.1.1

Factor $- 1$ out of $\sqrt{3}$ .

$\frac{- x (- 1 (- \sqrt{3}) + 1)}{- \sqrt{3} - 1} = \frac{- 1400}{- \sqrt{3} - 1}$

Step 1.4.3.2.1.2

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- x (- 1 (- \sqrt{3}) - 1 (- 1))}{- \sqrt{3} - 1} = \frac{- 1400}{- \sqrt{3} - 1}$

Step 1.4.3.2.1.3

Factor $- 1$ out of $- 1 (- \sqrt{3}) - 1 (- 1)$ .

$\frac{- x (- 1 (- \sqrt{3} - 1))}{- \sqrt{3} - 1} = \frac{- 1400}{- \sqrt{3} - 1}$

Step 1.4.3.2.1.4

Cancel the common factor.

$\frac{- x (- 1 (- \sqrt{3} - 1))}{- \sqrt{3} - 1} = \frac{- 1400}{- \sqrt{3} - 1}$

Step 1.4.3.2.1.5

Divide $- x \cdot (- 1)$ by $1$ .

$- x \cdot (- 1) = \frac{- 1400}{- \sqrt{3} - 1}$

Step 1.4.3.2.2

Multiply $- x (- 1)$ .

Tap for more steps...

Step 1.4.3.2.2.1

Multiply $- 1$ by $- 1$ .

$1 x = \frac{- 1400}{- \sqrt{3} - 1}$

Step 1.4.3.2.2.2

Multiply $x$ by $1$ .

$x = \frac{- 1400}{- \sqrt{3} - 1}$

Step 1.4.3.3

Simplify the right side.

Tap for more steps...

Step 1.4.3.3.1

Move the negative in front of the fraction.

$x = - \frac{1400}{- \sqrt{3} - 1}$

Step 1.4.3.3.2

Multiply $\frac{1400}{- \sqrt{3} - 1}$ by $\frac{- \sqrt{3} + 1}{- \sqrt{3} + 1}$ .

$x = - (\frac{1400}{- \sqrt{3} - 1} \cdot \frac{- \sqrt{3} + 1}{- \sqrt{3} + 1})$

Step 1.4.3.3.3

Multiply $\frac{1400}{- \sqrt{3} - 1}$ by $\frac{- \sqrt{3} + 1}{- \sqrt{3} + 1}$ .

$x = - \frac{1400 (- \sqrt{3} + 1)}{(- \sqrt{3} - 1) (- \sqrt{3} + 1)}$

Step 1.4.3.3.4

Expand the denominator using the FOIL method.

$x = - \frac{1400 (- \sqrt{3} + 1)}{{\sqrt{3}}^{2} - \sqrt{3} + \sqrt{3} - 1}$

Step 1.4.3.3.5

Simplify.

$x = - \frac{1400 (- \sqrt{3} + 1)}{2}$

Step 1.4.3.3.6

Cancel the common factor of $1400$ and $2$ .

Tap for more steps...

Step 1.4.3.3.6.1

Factor $2$ out of $1400 (- \sqrt{3} + 1)$ .

$x = - \frac{2 (700 (- \sqrt{3} + 1))}{2}$

Step 1.4.3.3.6.2

Cancel the common factors.

Tap for more steps...

Step 1.4.3.3.6.2.1

Factor $2$ out of $2$ .

$x = - \frac{2 (700 (- \sqrt{3} + 1))}{2 (1)}$

Step 1.4.3.3.6.2.2

Cancel the common factor.

$x = - \frac{2 (700 (- \sqrt{3} + 1))}{2 \cdot 1}$

Step 1.4.3.3.6.2.3

Rewrite the expression.

$x = - \frac{700 (- \sqrt{3} + 1)}{1}$

Step 1.4.3.3.6.2.4

Divide $700 (- \sqrt{3} + 1)$ by $1$ .

$x = - (700 (- \sqrt{3} + 1))$

Step 1.4.3.3.7

Apply the distributive property.

$x = - (700 (- \sqrt{3}) + 700 \cdot 1)$

Step 1.4.3.3.8

Multiply.

Tap for more steps...

Step 1.4.3.3.8.1

Multiply $- 1$ by $700$ .

$x = - (- 700 \sqrt{3} + 700 \cdot 1)$

Step 1.4.3.3.8.2

Multiply $700$ by $1$ .

$x = - (- 700 \sqrt{3} + 700)$

Step 1.4.3.3.9

Apply the distributive property.

$x = - (- 700 \sqrt{3}) - 1 \cdot 700$

Step 1.4.3.3.10

Multiply.

Tap for more steps...

Step 1.4.3.3.10.1

Multiply $- 700$ by $- 1$ .

$x = 700 \sqrt{3} - 1 \cdot 700$

Step 1.4.3.3.10.2

Multiply $- 1$ by $700$ .

$x = 700 \sqrt{3} - 700$

Step 1.5

The variable $y$ got canceled.

All real numbers

Step 2

Since $x = 700 \sqrt{3} - 700$ is a vertical line, there is no y-intercept and the slope is undefined.

Slope: Undefined

y-intercept: No y-intercept

Step 3

Find two points on the line.

$\begin{array}{c} x & y \\ 700 \sqrt{3} - 700 & 0 \\ 700 \sqrt{3} - 700 & 1 \end{array}$

Step 4

Graph the line using the slope, y-intercept, and two points.

Slope: Undefined

y-intercept: No y-intercept

$\begin{array}{c} x & y \\ 700 \sqrt{3} - 700 & 0 \\ 700 \sqrt{3} - 700 & 1 \end{array}$

Step 5