MATH 133 – Calculus with Fundamentals 1 Practice on Trigonometric Functions September 15, 2015

Background

In the video and class today, we have seen a “lightning review” of trigonometry. To practice on some ideas related to this, do the following problems.

Questions

1) Sinusoids

(a) Starting from the graph y = sin(x) and using ideas we have seen about scaling and shifting, sketch the graph y = 3 sin (\frac{x}{2}) − 1 on the interval [0, 8π].

(b) The graph in part (1) is an example of a sinusoid (or sine-wave graph). The amplitude of a sinusoid is one-half the vertical distance between the minimum and maximum values. What is the amplitude of your sinusoid in (1)?

(c) The period of a sinusoid f(x) is the smallest strictly positive number T for which it is true that f(x + T) = f(x) for all x. For example the period of f(x) = cos(x) is T = 2π. What is the period of the sinusoid from part (1)?

(d) Give a formula defining a sinusoid with amplitude A = 7 and period T = 5π.

2) By plotting points with 0 < x < π, sketch the graph y = cot(x) = \frac{cos(x)}{sin(x)}. How are tan (x − \frac{π}{2} ) and cot(x) related?