Trigonometry Examples

Solve for θ in Degrees 2sin(theta)=-1
Step 1
Divide each term in by and simplify.
Tap for more steps...
Step 1.1
Divide each term in by .
Step 1.2
Simplify the left side.
Tap for more steps...
Step 1.2.1
Cancel the common factor of .
Tap for more steps...
Step 1.2.1.1
Cancel the common factor.
Step 1.2.1.2
Divide by .
Step 1.3
Simplify the right side.
Tap for more steps...
Step 1.3.1
Move the negative in front of the fraction.
Step 2
Take the inverse sine of both sides of the equation to extract from inside the sine.
Step 3
Simplify the right side.
Tap for more steps...
Step 3.1
The exact value of is .
Step 4
The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from , to find a reference angle. Next, add this reference angle to to find the solution in the third quadrant.
Step 5
Simplify the expression to find the second solution.
Tap for more steps...
Step 5.1
Subtract from .
Step 5.2
The resulting angle of is positive, less than , and coterminal with .
Step 6
Find the period of .
Tap for more steps...
Step 6.1
The period of the function can be calculated using .
Step 6.2
Replace with in the formula for period.
Step 6.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 6.4
Divide by .
Step 7
Add to every negative angle to get positive angles.
Tap for more steps...
Step 7.1
Add to to find the positive angle.
Step 7.2
Subtract from .
Step 7.3
List the new angles.
Step 8
The period of the function is so values will repeat every degrees in both directions.
, for any integer