Trigonometry Examples

Find All Complex Solutions 4sin(x)=-cos(x)^2+4
Step 1
Move all the expressions to the left side of the equation.
Tap for more steps...
Step 1.1
Add to both sides of the equation.
Step 1.2
Subtract from both sides of the equation.
Step 2
Replace with .
Step 3
Solve for .
Tap for more steps...
Step 3.1
Simplify the left side.
Tap for more steps...
Step 3.1.1
Apply pythagorean identity.
Step 3.2
Replace the with based on the identity.
Step 3.3
Subtract from .
Step 3.4
Add to both sides of the equation.
Step 3.5
Divide each term in by and simplify.
Tap for more steps...
Step 3.5.1
Divide each term in by .
Step 3.5.2
Simplify the left side.
Tap for more steps...
Step 3.5.2.1
Dividing two negative values results in a positive value.
Step 3.5.2.2
Divide by .
Step 3.5.3
Simplify the right side.
Tap for more steps...
Step 3.5.3.1
Divide by .
Step 3.6
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.7
Simplify .
Tap for more steps...
Step 3.7.1
Rewrite as .
Step 3.7.2
Rewrite as .
Step 3.7.3
Rewrite as .
Step 3.8
The complete solution is the result of both the positive and negative portions of the solution.
Tap for more steps...
Step 3.8.1
First, use the positive value of the to find the first solution.
Step 3.8.2
Next, use the negative value of the to find the second solution.
Step 3.8.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 3.9
Set up each of the solutions to solve for .
Step 3.10
Solve for in .
Tap for more steps...
Step 3.10.1
Take the inverse sine of both sides of the equation to extract from inside the sine.
Step 3.10.2
The inverse sine of is undefined.
Undefined
Undefined
Step 3.11
Solve for in .
Tap for more steps...
Step 3.11.1
Take the inverse sine of both sides of the equation to extract from inside the sine.
Step 3.11.2
The inverse sine of is undefined.
Undefined
Undefined
Step 3.12
List all of the solutions.
No solution
No solution