Question

Given: y=2cos1/2( θ+π/4 )+1 find:

a. amplitude
b. number of cycles
c. horizontal shift
d. vertical shift
e. graph

Answer 1

What do you think the answer is?

Answer 2

openstudy is my last resort, ive been trying to figure this out for 6 weeks. i have the graph down and the amplitude but that is about it.

Answer 3

In your equation, is that 1/2 a power or is it inside the cos() function?

Answer 4

cos() function

Answer 5

Is the +1 inside or outside?

Answer 6

I've gotta go soon so we're gonna have to be quick here.

Answer 7

outside

Answer 8

i just got the vertical shift

Answer 9

When you shift \(f(x)\) RIGHT by \(a\) is becomes \(f(x-a)\). For a left shift, it is \(f(x+a)\).

So to find a horizontal shift, we look what \(x\) has been replaced with. In this case, it's \(x+\frac{\pi}{4}\). What is our shift?

Answer 10

Just read this: http://www.regentsprep.org/regents/math/algtrig/att7/sinusoidal.htm

Answer 11

I'm going now. Here's the answers if you want to check yours:

a. 2
b. 0.5 cycles of period 4pi
c. -pi/4
d. 1
e. https://i.imgur.com/xNGGLyx.png
red your graph, green is just cos(x) for comparison.