Trigonometry Examples

Solve for x 9cos(x)^2+18cos(x)+9=0
Step 1
Substitute for .
Step 2
Factor the left side of the equation.
Tap for more steps...
Step 2.1
Factor out of .
Tap for more steps...
Step 2.1.1
Factor out of .
Step 2.1.2
Factor out of .
Step 2.1.3
Factor out of .
Step 2.1.4
Factor out of .
Step 2.1.5
Factor out of .
Step 2.2
Factor using the perfect square rule.
Tap for more steps...
Step 2.2.1
Rewrite as .
Step 2.2.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 2.2.3
Rewrite the polynomial.
Step 2.2.4
Factor using the perfect square trinomial rule , where and .
Step 3
Divide each term in by and simplify.
Tap for more steps...
Step 3.1
Divide each term in by .
Step 3.2
Simplify the left side.
Tap for more steps...
Step 3.2.1
Cancel the common factor of .
Tap for more steps...
Step 3.2.1.1
Cancel the common factor.
Step 3.2.1.2
Divide by .
Step 3.3
Simplify the right side.
Tap for more steps...
Step 3.3.1
Divide by .
Step 4
Set the equal to .
Step 5
Subtract from both sides of the equation.
Step 6
Substitute for .
Step 7
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Step 8
Simplify the right side.
Tap for more steps...
Step 8.1
The exact value of is .
Step 9
The cosine function is negative in the second and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Step 10
Subtract from .
Step 11
Find the period of .
Tap for more steps...
Step 11.1
The period of the function can be calculated using .
Step 11.2
Replace with in the formula for period.
Step 11.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 11.4
Divide by .
Step 12
The period of the function is so values will repeat every radians in both directions.
, for any integer