Trigonometry Examples

Solve for θ in Radians 4sin(theta)^2-4sin(theta)+1=0
Step 1
Substitute for .
Step 2
Factor using the perfect square rule.
Tap for more steps...
Step 2.1
Rewrite as .
Step 2.2
Rewrite as .
Step 2.3
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 2.4
Rewrite the polynomial.
Step 2.5
Factor using the perfect square trinomial rule , where and .
Step 3
Set the equal to .
Step 4
Solve for .
Tap for more steps...
Step 4.1
Add to both sides of the equation.
Step 4.2
Divide each term in by and simplify.
Tap for more steps...
Step 4.2.1
Divide each term in by .
Step 4.2.2
Simplify the left side.
Tap for more steps...
Step 4.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 4.2.2.1.1
Cancel the common factor.
Step 4.2.2.1.2
Divide by .
Step 5
Substitute for .
Step 6
Take the inverse sine of both sides of the equation to extract from inside the sine.
Step 7
Simplify the right side.
Tap for more steps...
Step 7.1
The exact value of is .
Step 8
The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second quadrant.
Step 9
Simplify .
Tap for more steps...
Step 9.1
To write as a fraction with a common denominator, multiply by .
Step 9.2
Combine fractions.
Tap for more steps...
Step 9.2.1
Combine and .
Step 9.2.2
Combine the numerators over the common denominator.
Step 9.3
Simplify the numerator.
Tap for more steps...
Step 9.3.1
Move to the left of .
Step 9.3.2
Subtract from .
Step 10
Find the period of .
Tap for more steps...
Step 10.1
The period of the function can be calculated using .
Step 10.2
Replace with in the formula for period.
Step 10.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 10.4
Divide by .
Step 11
The period of the function is so values will repeat every radians in both directions.
, for any integer