Review for Test 3, Math 1330

1. Evaluate the following:

2(sin(225°) − cos(120°))

3p tan2 ( ) 4 11p cos2 ( ) 6

cot(180°)

sin(225) + cos (45)  tan(315)

5p sin 6 4p cos 3

3 tan(sin-1 ( )) 11

cos(sin-1 (.5))

2. State the trigonometric area of a triangle formula. Given a triangle ABC with angle A measuring 120°, side AB = 5cm and side AC = 8 cm, what is the area of the triangle?

3. Suppose x is an acute angle and tan(x) = 1/7. What is sec(x)?

4. Suppose ΔABC is a right triangle with m A =n 90°. If side BA = 5 cm and side BC = 7 cm, what are the trigonometric functions for C ?

sin(- x + 200 p )( - sin(x))

1 5. List two vertical asymptotes for

cot(x)

sec(2x)

p csc(x+ ) 3

6. Short answer questions:

Where is f(x) = tanx an increasing function on the interval [0, 2 p )?

Where does f(x) = cos(2x) decrease on (− p, p )?

Where are the turnaround points for f(x) = sin(2x) on [0, 3 p ]?

p Give the the following facts for :f (x)= - 3cos(2x + ) 3 Domain, range, y-intercept, x-intercepts, all asymptotes.

Give the period and two vertical asymptotes for f(x) = tan(2x).

p Is the point (0, −1) on the graph of f (x)= cos( x + p ) ? 3 p p Is the point ( ,0) on the graph of f (x)= sin(3x + ) ? 3 2

2 7. What is the equation for the following graphs?

p a. There are VAs at . 2

p b. The point ( ,3) is on the graph 8

3 c. The point (4, −2) is on the graph.

8. Sketch the following graphs. List the domain, the range, at least 3 x-intercepts, the y-intercept, and at least 3 asymptotes. If there is not at least one of an item, say so.

x p 2sin(+ ) 2 3

sin-1 (x)

tan(x)

-cos(3x)

3sec( px )

4 9. Given ABC with mB = 135, side AB measures 9 inches, and side BC measures 4 inches. What is the area of the triangle.

3p 10. Find the trigonometric functions for : if sin = ¼ and < q <2 p . 2

13. Verify the identity:

csc2 x- 1 a. = cos2 x csc2 x

5 b. (sec2 x- 1)(csc 2 x - 1) = 1

cos x cot x- sin x tan x c. =1 + sin x cos x hint: x3- y 3 = (x - y)(x 2 + xy + y 2 ) csc x- sec x