Trigonometry Examples

Solve over the Interval sin(x+pi/4)+sin(x-pi/4)=-1 , [0,2pi)
,
Step 1
Graph each side of the equation. The solution is the x-value of the point of intersection.
, for any integer
Step 2
Find the values of that produce a value within the interval .
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Step 2.1
Plug in for and simplify to see if the solution is contained in .
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Step 2.1.1
Plug in for .
Step 2.1.2
Simplify.
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Step 2.1.2.1
Multiply .
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Step 2.1.2.1.1
Multiply by .
Step 2.1.2.1.2
Multiply by .
Step 2.1.2.2
Add and .
Step 2.1.3
The interval contains .
Step 2.2
Plug in for and simplify to see if the solution is contained in .
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Step 2.2.1
Plug in for .
Step 2.2.2
Simplify.
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Step 2.2.2.1
Multiply .
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Step 2.2.2.1.1
Multiply by .
Step 2.2.2.1.2
Multiply by .
Step 2.2.2.2
Add and .
Step 2.2.3
The interval contains .
Step 3