Basic Trigonometric Functions

Basic Trigonometric Functions Math Questions

Complete the following questions without the use of a calculator. You must justify your answer using either the Unit Circle or right triangles. Answer without supporting work will receive no credit.

1. Given csc = - 7 and that n < < 3? 2 find the following values:

sin = csc cos = sec 0 = tan = cot A =

2. Find the exam values of the following trigonometric functions. Include a diagram indicating the angle and the reference angle.

sin(210°) = tan() (f tan(71) = coscana) - tan(*) 2 sin 5? 3 1

3. Sketch the graph of the following basic trigonometric functions. On each of the graphs label the coordinates of all x-intercepts, y-intercepts, local maxima and minima, and asymptotes as appropriate. Also state the domain and range of each function.

f(x) = sinx A+ Range: Domain: f(x) = cosx (? Domain: f(x) = tanx Range:_ A+ Domain: Range: 2

Graphical Limits

4. Sketch the graph of one function with all of the following properties. Be sure use labels and tick marks on your graph that is submitted for grading.

lim f(x) = 0 lim f(x) = 5 x-5 x2 lim f(x) = -1 f(-5) = lim f(x) x2 x2 lim f(x) = -4 lim f(x) = -00 5 3+ 2+ 1+ 8 -7 6 -5 4 _3 -2 -1 2 3 4 5 6 7 x -2+ 3 5. Use the graph below to evaluate the following limits. You do NOT need to show any work for this question. 3 1 8 6 -2 4 8 -1 1 2- -3 -4 1 1 ! i ! i 1 1 ! -5 1 I a = -6 a = -4 a = 2 a = 4 a = 5 lim f(x) xa lim f (x) xa lim f (x) xa f(a) lim f(x) = lim f(x) = 4 6. Determine the graphical feature illustrated by the given limit and function values. lim f(x) = 7 At x = 5, the graph has a: x → 5 ||(5) = -2 Removable discontinuity (hole) Jump discontinuity Vertical asymptote Horizontal asymptote Continuous at x = 5 lim f(x) = 9 At x = 2, the graph has a: x2 |(2) = 9 Removable discontinuity (hole) Jump discontinuity Vertical asymptote Horizontal asymptote Continuous at x = 2 lim f(x) = 0 At x = -6, the graph has a: X-6 f(-6) = 5 Removable discontinuity (hole) Jump discontinuity Vertical asymptote Horizontal asymptote Continuous at x = -6 lim f(x) = 0 At x = -3, the graph has a: Removable discontinuity (hole) Jump discontinuity Vertical asymptote Horizontal asymptote Continuous at x = -3 lim f(x) = -4 x-3 (-3) = -4 lim f(x) = -3 As x → -00, the graph has a: Removable discontinuity (hole) Jump discontinuity Vertical asymptote Horizontal asymptote Continuous at x = -3 5