How are you expected to be able to graph this graph without a calculator.
How would you find the endpoints and xintercepts and yintercepts
First, we see that the amplitude is 5, because the max and min of any non-dilated cosine graph is [-1,1]
The period is calculated by 2pi/n, so the period in our case is 2pi/2 (the number before x) = pi
That means we're going through two revolutions of the graph through the domain [-pi,pi]
To find the endpoints, we sub in x= -pi and x = pi into the equation, then solve.
f(pi) = 5cos(2(4pi/3)) = 5cos(8pi/3) = 5cos(2pi + 2pi/3) = 5cos(2pi/3) = -5/2
To find the x-intercepts, we sub in y=0 into the equation, so 5cos(2(x+pi/3)) = 0
cos(2(x+pi/3))=0
inverse cos (0) = 2(x+pi/3) = pi/2, 3pi/2, 5pi/2, -pi/2
x+pi/3 = pi/4, 3pi/4, 5pi/4, -pi/4
x= -pi/12, 5pi/12, 11pi/12, -7pi/12
To find the y-intercepts we sub in x=0 into the equation and do the same process
And then to graph you just have to know how to draw a regular cos graph and use the endpoints and intercepts as a guide!