Trigonometry Examples

$r + r \sin (θ) = 1$

Step 1

Solve the equation for $r$ .

Tap for more steps...

Step 1.1

Factor $r$ out of $r + r \sin (θ)$ .

Tap for more steps...

Step 1.1.1

Raise $r$ to the power of $1$ .

$r + r \sin (θ) = 1$

Step 1.1.2

Factor $r$ out of $r^{1}$ .

$r \cdot 1 + r \sin (θ) = 1$

Step 1.1.3

Factor $r$ out of $r \sin (θ)$ .

$r \cdot 1 + r (\sin (θ)) = 1$

Step 1.1.4

Factor $r$ out of $r \cdot 1 + r (\sin (θ))$ .

$r (1 + \sin (θ)) = 1$

Step 1.2

Divide each term in $r (1 + \sin (θ)) = 1$ by $1 + \sin (θ)$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $r (1 + \sin (θ)) = 1$ by $1 + \sin (θ)$ .

$\frac{r (1 + \sin (θ))}{1 + \sin (θ)} = \frac{1}{1 + \sin (θ)}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $1 + \sin (θ)$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{r (1 + \sin (θ))}{1 + \sin (θ)} = \frac{1}{1 + \sin (θ)}$

Step 1.2.2.1.2

Divide $r$ by $1$ .

$r = \frac{1}{1 + \sin (θ)}$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $r$ is $1$ , the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not a linear equation.

Not Linear