Homework Assignment #3 Section 5.5

I graded problems 6, 8, and 49.

Problem 6:

y = 1 sec (1 p x). Determine the vertical asymptotes:

-p /2 £ 1 p x £ p /2

(Consecutive zeros of cos q at [-p /2, p /2])

-p /2(2/p ) £ x £ p /2(2/p )

Consecutive asymptotes representing half of one period:

-1 £ x £ 1.

One period is therefore 4 units in length.

(h) is the correct graph. Note the amplitude, 1 .

Problem 8:

y = -2 sec (2p x). Determine the vertical asymptotes first.

Consecutive zeros of cos q at [-p /2, p /2]:

-p /2 £ 2p x £ p /2

 

-p /2(1/(2p )) £ x £ p /2(1/(2p ))

Consecutive asymptotes representing
half of one period occur at x = -1/4, 1/4.

-1/4 £ x £ 1/4.
One period is therefore 1 unit in length.

(c) is the correct graph. Note the amplitude, |-2|, and the reflection about the x-axis.

 

Problem 49:

2 sin(x) is greater than 1 csc(x) from p /6 to 5p /6, just plot both functions in the same viewing window and select 2nd Calc Intersect to determine the points of intersection. The sine approaches 0 and the cosecant approaches infinity as x approaches p, as these are reciprocal functions.

Essential Trigonometry, Math Links

by Jack Tompkins