Trigonometry Examples

Find the x and y Intercepts h(x)=2cos(2x-pi)+4
Step 1
Find the x-intercepts.
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Step 1.1
To find the x-intercept(s), substitute in for and solve for .
Step 1.2
Solve the equation.
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Step 1.2.1
Rewrite the equation as .
Step 1.2.2
Subtract from both sides of the equation.
Step 1.2.3
Divide each term in by and simplify.
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Step 1.2.3.1
Divide each term in by .
Step 1.2.3.2
Simplify the left side.
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Step 1.2.3.2.1
Cancel the common factor of .
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Step 1.2.3.2.1.1
Cancel the common factor.
Step 1.2.3.2.1.2
Divide by .
Step 1.2.3.3
Simplify the right side.
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Step 1.2.3.3.1
Divide by .
Step 1.2.4
The range of cosine is . Since does not fall in this range, there is no solution.
No solution
No solution
Step 1.3
To find the x-intercept(s), substitute in for and solve for .
x-intercept(s):
x-intercept(s):
Step 2
Find the y-intercepts.
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Step 2.1
To find the y-intercept(s), substitute in for and solve for .
Step 2.2
Solve the equation.
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Step 2.2.1
Remove parentheses.
Step 2.2.2
Simplify .
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Step 2.2.2.1
Simplify each term.
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Step 2.2.2.1.1
Multiply by .
Step 2.2.2.1.2
Subtract from .
Step 2.2.2.1.3
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.
Step 2.2.2.1.4
The exact value of is .
Step 2.2.2.1.5
Multiply .
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Step 2.2.2.1.5.1
Multiply by .
Step 2.2.2.1.5.2
Multiply by .
Step 2.2.2.2
Add and .
Step 2.3
y-intercept(s) in point form.
y-intercept(s):
y-intercept(s):
Step 3
List the intersections.
x-intercept(s):
y-intercept(s):
Step 4