http://www.ck12.org Chapter 5. Trigonometric Functions
- Graph the functionf(x) =− 5 ·sec(π 3 (x− 2 ))−4.
- Where are the asymptotes for tangent and why do they occur?
Answers: - If you connect the relative maximums and minimums of the function, it produces a shifted cosine curve that is
easier to work with.
The amplitude is 3. The vertical shift is 2 down. The period is 4 which implies thatb=π 2. The shape is
positive cosine and if you choose to start atx=0 there is no phase shift.
f(x) = 3 ·csc(π 2 x)− 2- First graph the function as if it were a cosine. The vertical shift is -4. The horizontal shift is to the right 2. This
gives a starting point for the period. Sinceb=π 3 the period must be 6.