In Exercises 16 and 17 use a graphing utility to graph the f

In Exercises 16 and 17, use a graphing utility to graph the function. If the function is periodic, find its period. y = sin 2 pi x + 2 cos pi x y = 6e^-0.12t cos(0.25t), 0 lessthanorequalto t lessthanorequalto 32 Find a, b, and c for the function f(x) = a sin(bx + c) such that the graph of f matches the graph at the right. Find the exact value of tan(arccos 2/3) without using a calculator. In Exercises 20-22, use a graphing utility to graph the function. f(x) = 2 aresin(1/2 x) f(x) = 2 arccos x f(x) = arctan x/2 A plane is 160 miles north and 110 miles cast of an airport. What hearing should be taken to fly directly to the airport?

Solution

Question 18)

The point (-pi/2, 2) tells us that amplitude of the graph is 2. Therefore, value of a is 2.

Period of function is 8pi. Thereofre, b = 2pi/8pi = 1/4

And, we can see that graph is shifted to left by 3pi/2, therefore c/b = 3pi/2

4c = 3pi/2

c = 3pi/8

Therefore, the required equation will be f(x) = 2sin((1/4)x+3pi/8))

Question 19:

Say y=tan(arccos(2/3))

Further, say arccos(2/3) = x

Therefore, cos(x) = 2/3

Hence, tan(x) = sqrt(5)/2

Therefore, tan(x) = tan(arccos(2/3)) = sqrt(5)/2