Pearson Algebra 2 Common Core, 2011
PA
Pearson Algebra 2 Common Core, 2011 View details
2. Solving Trigonometric Equations Using Inverses
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Exercise 54 Page 917

The intercepts of the graph of a function occur when

radians, radians, for any integer

Practice makes perfect
The intercepts of the graph of a function occur when Let's substitute for into the given equation.
We will start by solving the equation for
Solve for
To find a solution for this equation, we will use an inverse trigonometric function and a calculator.

One solution to is To find the second solution for this equation, we need to use the unit circle. Remember, cosine is negative in the second and third quadrants of the coordinate plane.

The cosine of an angle in standard position is the coordinate of the point of intersection of the unit circle and the terminal side of the angle. The solution is in Quadrant II, so the second solution must be in Quadrant III. Because these angles are symmetric across the axis and a full turn measures radians, to find this angle we subtract from

We found two solutions to the given equation, and Finally, keep in mind that if we add or subtract a multiple of radians, the terminal side of the angle will be in the same position. Therefore, the resulting angles will also be solutions to the equation.
These are the intercepts of the graph of