Name Date

Practice 7.7: Graphs of Tan, Cot, Csc & Sec

1. Find the period and amplitude of each function.

a. y =2tan (2x) b. y = -3csc

2

x c. y =

2

5cot (4πx) d. y = -2sec

2

x

2. Match the trig function with its graph. The graphs have different widows.

i. y = sec 2x

ii. y = tan 3x

iii. y = tan 2

x

iv. y = 2csc 2

x

v. y = cot πx

vi. y = 2

1sec πx

vii. y = -sec x

viii. y = -2csc 2πx

3. Sketch the functions to determine if they are; odd, even or neither.

a. f(x) = tan x b. f(x) = sin x

c. f(x) =cos x d. f(x) = cot x

4. Sketch the graphs. Include 2 periods.

a. y = 1/4tan x b. y = tan 2x

c. y = -3tan πx d. y = -1/2sec x

e. y = 2sec 4x + 1 f. y = csc 3

x

g. y = cot 2

x h. y = 3cot

2

x

5. A plane flying at an altitude of 6miles over level ground will pass directly over a radar

antenna. Let d be the distance on the ground from the antenna to a point directly

under the plane and let x be the angle of elevation to the plane from the antenna.

Write d as a function of x and graph the function over the interval 0 < x < 2π.

6. A TV camera is on a reviewing platform 100m from the street where a parade will

pass by left to right. Express the distance d from the camera to a particular float in

the parade as a function of the angle x , and graph the function over

the interval -π/2 < x <

π/2. (conxider x as negative when a float approaches from the

left.