Solve for x in Degrees 5tan(x)sin(x)-4sin(x)=0

Solve Math

Trigonometry

$5 \tan (x) \sin (x) - 4 \sin (x) = 0$

Simplify the left side of the equation.

Tap for more steps...

Simplify each term.

Tap for more steps...

Rewrite $\tan (x)$ in terms of sines and cosines.

$5 (\frac{\sin (x)}{\cos (x)}) \cdot \sin (x) - 4 \sin (x) = 0$

Combine $5$ and $\frac{\sin (x)}{\cos (x)}$ .

$\frac{5 \sin (x)}{\cos (x)} \cdot \sin (x) - 4 \sin (x) = 0$

Multiply $\frac{5 \sin (x)}{\cos (x)} \sin (x)$ .

Tap for more steps...

Combine $\frac{5 \sin (x)}{\cos (x)}$ and $\sin (x)$ .

$\frac{5 \sin (x) \sin (x)}{\cos (x)} - 4 \sin (x) = 0$

Raise $\sin (x)$ to the power of $1$ .

$\frac{5 (\sin (x) \sin (x))}{\cos (x)} - 4 \sin (x) = 0$

Raise $\sin (x)$ to the power of $1$ .

$\frac{5 (\sin (x) \sin (x))}{\cos (x)} - 4 \sin (x) = 0$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5 {\sin (x)}^{1 + 1}}{\cos (x)} - 4 \sin (x) = 0$

Add $1$ and $1$ .

$\frac{5 \sin^{2} (x)}{\cos (x)} - 4 \sin (x) = 0$

Simplify each term.

Tap for more steps...

Factor $\sin (x)$ out of $\sin^{2} (x)$ .

$\frac{5 (\sin (x) \sin (x))}{\cos (x)} - 4 \sin (x) = 0$

Separate fractions.

$\frac{5 (\sin (x))}{1} \cdot \frac{\sin (x)}{\cos (x)} - 4 \sin (x) = 0$

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

$\frac{5 (\sin (x))}{1} \cdot \tan (x) - 4 \sin (x) = 0$

Divide $5 (\sin (x))$ by $1$ .

$5 \sin (x) \tan (x) - 4 \sin (x) = 0$

Factor $\sin (x)$ out of $5 \sin (x) \tan (x) - 4 \sin (x)$ .

Tap for more steps...

Factor $\sin (x)$ out of $5 \sin (x) \tan (x)$ .

$\sin (x) (5 \tan (x)) - 4 \sin (x) = 0$

Factor $\sin (x)$ out of $- 4 \sin (x)$ .

$\sin (x) (5 \tan (x)) + \sin (x) \cdot - 4 = 0$

Factor $\sin (x)$ out of $\sin (x) (5 \tan (x)) + \sin (x) \cdot - 4$ .

$\sin (x) (5 \tan (x) - 4) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$\sin (x) = 0$

$5 \tan (x) - 4 = 0$

Set $\sin (x)$ equal to $0$ and solve for $x$ .

Tap for more steps...

Set $\sin (x)$ equal to $0$ .

$\sin (x) = 0$

Solve $\sin (x) = 0$ for $x$ .

Tap for more steps...

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

$x = \arcsin (0)$

Simplify the right side.

Tap for more steps...

The exact value of $\arcsin (0)$ is $0$ .

$x = 0$

The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from $180$ to find the solution in the second quadrant.

$x = 180 - 0$

Subtract $0$ from $180$ .

$x = 180$

Find the period of $\sin (x)$ .

Tap for more steps...

The period of the function can be calculated using $\frac{360}{| b |}$ .

$\frac{360}{| b |}$

Replace $b$ with $1$ in the formula for period.

$\frac{360}{| 1 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{360}{1}$

Divide $360$ by $1$ .

$360$

The period of the $\sin (x)$ function is $360$ so values will repeat every $360$ degrees in both directions.

$x = 360 n, 180 + 360 n$ , for any integer $n$

Set $5 \tan (x) - 4$ equal to $0$ and solve for $x$ .

Tap for more steps...

Set $5 \tan (x) - 4$ equal to $0$ .

$5 \tan (x) - 4 = 0$

Solve $5 \tan (x) - 4 = 0$ for $x$ .

Tap for more steps...

Add $4$ to both sides of the equation.

$5 \tan (x) = 4$

Divide each term in $5 \tan (x) = 4$ by $5$ and simplify.

Tap for more steps...

Divide each term in $5 \tan (x) = 4$ by $5$ .

$\frac{5 \tan (x)}{5} = \frac{4}{5}$

Simplify the left side.

Tap for more steps...

Cancel the common factor of $5$ .

Tap for more steps...

Cancel the common factor.

$\frac{5 \tan (x)}{5} = \frac{4}{5}$

Divide $\tan (x)$ by $1$ .

$\tan (x) = \frac{4}{5}$

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

$x = \arctan (\frac{4}{5})$

Simplify the right side.

Tap for more steps...

Evaluate $\arctan (\frac{4}{5})$ .

$x = 38.65980825$

The tangent function is positive in the first and third quadrants. To find the second solution, subtract the reference angle from $180$ to find the solution in the fourth quadrant.

$x = 180 + 38.65980825$

Add $180$ and $38.65980825$ .

$x = 218.65980825$

Find the period of $\tan (x)$ .

Tap for more steps...

The period of the function can be calculated using $\frac{180}{| b |}$ .

$\frac{180}{| b |}$

Replace $b$ with $1$ in the formula for period.

$\frac{180}{| 1 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{180}{1}$

Divide $180$ by $1$ .

$180$

The period of the $\tan (x)$ function is $180$ so values will repeat every $180$ degrees in both directions.

$x = 38.65980825 + 180 n, 218.65980825 + 180 n$ , for any integer $n$

The final solution is all the values that make $\sin (x) (5 \tan (x) - 4) = 0$ true.

$x = 360 n, 180 + 360 n, 38.65980825 + 180 n, 218.65980825 + 180 n$ , for any integer $n$

Consolidate the answers.

Tap for more steps...

Consolidate $360 n$ and $180 + 360 n$ to $180 n$ .

$x = 180 n, 38.65980825 + 180 n, 218.65980825 + 180 n$ , for any integer $n$

Consolidate $38.65980825 + 180 n$ and $218.65980825 + 180 n$ to $38.65980825 + 180 n$ .

$x = 180 n, 38.65980825 + 180 n$ , for any integer $n$

Do you know how to Solve for x in Degrees 5tan(x)sin(x)-4sin(x)=0? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.