# How do you graph #y=sectheta+2#?

##### 1 Answer

Dec 11, 2017

#### Answer:

See below.

#### Explanation:

- Graph the function first as if it were a cosine function. This is because secant is the inverse of cosine.
- Begin with the reference y= d+a cos (bx-c).
- The absolute value of a is your amplitude (in this case, it's an understood 1). This is one-half the distance between the highest and lowest points of the graph.
- If graphing in degrees, your period is 360/b, or in this case 360. (If in radians, use 2
#pi# , which is equivalent to 360 degrees). - The horizontal translation, or phase shift, is equal to -c/b. In this case, it's 0 because there is no c or b. There is no horizontal translation.
- The vertical translation is equal to d, or in this case, +2.
- Graph it like a COSINE function.
- Make a t-table with your points.
- Your first point is equal to your horizontal translation, or in this case 0.
- Your end point is equal to your horizontal translation plus your period, or in this case, 360 (or 2
#pi# if graphing in radians). - Your increments are gained by dividing your period by 4. (in this case, 90).
- Your points on the x side of your t-table will be 0, 90, 180, 270, and 360 in this case. That is one full cycle of the function.
- Use a calculator to get your y points, being careful with parentheses. If you can't use a calculator, do translations on the parent function. y=cos(x)
- Graph the COSINE function, but don't connect the dots.
- Every HIGH point on the graph will be a parabola opening UP.
- Every LOW point on the graph will be a parabola opening DOWN.
- Every MIDDLE point is an asymptote . Draw a vertical dashed line here.
- You've now graphed a secant graph with a vertical translation of +2!