Basic Trig Functions Question (1 Viewer)

[ThreeOne]

For the graph y=cos x
.................................2

Will the graph intercept the y-axis at 1?

If the amplitude is 1, will cos x graphs always intercept at y=1?


And for the graph y=cos(x+pi/4), what is the period and how do you work it out?

 

[coblin]

The graph with intercept the y-axis at y=1. (0,1)

If the amplitude is 1, all graphs of the form y = cos(ax) will have a y-intercept of (0,1), because the y-intercept as at x=0. x=0 causes y= cos(ax) = cos(0) = 1.

y=cos(x+pi/4) has not changed it's period. It has been translated to the left pi/4 units. Think about the shape of the cos graph. Does adding pi/4 to the x values change the shape of the graph? Nope, it only moves it sideways, but doesn't squash or stretch it, so the period stays the same.

To figure out period for sin(ax) and cos(ax), the formula is 2pi/a

 

[ThreeOne]

Ok thanks.

Can someone help me with this question, please?;

Find the maximum and minimum values for y=sin2x in the domain 0<x<Pi

 

[201055]

Haven't done these for a while, gonna have a crack at it

y = sin 2x
y' = 2 cos 2x

When y'=0,

2cos2x = 0
2x = pi/2 (Limit given, x between 0 and pi)
x = pi/4

Test:
When x less than pi/4 = +ve
When x larger than pi/4 = -ve

Hence, x= pi/4 is a max value

 

[beentherdunthat]

Just a note for this question
If the amplitude is 1, will cos x graphs always intercept at y=1?

Sometimes the amp is 1 yeah, but if it's a function like f(x)=Cos (x) + 1 say than it will intercept at (0,2) for the Y-Axis.
This is your typical shifting of the graph question. The cos graph is shifted up by 1.