Trigonometry Examples

Solve for s cos(s)=-1/2
cos(s)=-12
Step 1
Take the inverse cosine of both sides of the equation to extract s from inside the cosine.
s=arccos(-12)
Step 2
Simplify the right side.
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Step 2.1
The exact value of arccos(-12) is 2π3.
s=2π3
s=2π3
Step 3
The cosine function is negative in the second and third quadrants. To find the second solution, subtract the reference angle from 2π to find the solution in the third quadrant.
s=2π-2π3
Step 4
Simplify 2π-2π3.
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Step 4.1
To write 2π as a fraction with a common denominator, multiply by 33.
s=2π33-2π3
Step 4.2
Combine fractions.
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Step 4.2.1
Combine 2π and 33.
s=2π33-2π3
Step 4.2.2
Combine the numerators over the common denominator.
s=2π3-2π3
s=2π3-2π3
Step 4.3
Simplify the numerator.
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Step 4.3.1
Multiply 3 by 2.
s=6π-2π3
Step 4.3.2
Subtract 2π from 6π.
s=4π3
s=4π3
s=4π3
Step 5
Find the period of cos(s).
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Step 5.1
The period of the function can be calculated using 2π|b|.
2π|b|
Step 5.2
Replace b with 1 in the formula for period.
2π|1|
Step 5.3
The absolute value is the distance between a number and zero. The distance between 0 and 1 is 1.
2π1
Step 5.4
Divide 2π by 1.
2π
2π
Step 6
The period of the cos(s) function is 2π so values will repeat every 2π radians in both directions.
s=2π3+2πn,4π3+2πn, for any integer n
 [x2  12  π  xdx ]