Trigonometry Examples

Solve over the Interval cos(theta)-4=-3 , [0,2pi)
,
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
Add and .
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
The exact value of is .
The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
Subtract from .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
Consolidate the answers.
, for any integer
Plug in for and simplify to see if the solution is contained in .
Plug in for .
Simplify.
Multiply .
Multiply by .
Multiply by .
Add and .
The interval contains .
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