Hi guys! Last friday, we were finishing up the topic about Sinusoidal Functions.

Let's take a recap about how to create equations for sinusoidal functions.

1. First, we have to find the middle axis (this will be d-value)
   
2. Find the amplitude (this will be the a-value). The easiest way to find the amplitude is to count from the middle axis to the highest point the graph is reached)
   
3. Determine the period and then calculate the b-value.
   
4. Identify the type of original wave (it's either y=sinx or y=cosx)
   
5. Create the first equation using the a, b, c and d values
   
6. Create the second and third equations including the a,b,c and d values.

So for example.

1. The middle axis will be at 0 which makes the d value = 0

2. Amplitude = 1

3. Period = 2π so b value will equal to 1

4. The type of original wave for this graph would be y=cosx

5. So now, we will create our three equations

I. y=cosx

II y=sin(x-)

iii. y=-sin(x+)

Note: Your goal is to manipulate the type of function you`re working with for the second and third equations by making it mask the original equation. Also, when creating the two other equations after determining the equation for the sinusoidal function, the two equations have to be the opposite or the other function that was not the original. If the original function was cos, then the two other equations would be sin. And vice versa.

The other thing we learned about is solving functions which involves some of the stuff we learned from Unit 1: circular functions

For example: p(x)=-cos(x+5) - 2

Things to keep in mind: special triangles and quadrantals.

p(0) = - cos(0+5) - 2 I put x to 0

= - cos(5) - 2

Multiply 5 by which becomes ⁵

= -cos ⁵ - 2

** Cos = adj/hyp so ⁵ = 1/2 but since cos was -'ve then 1/2 would be -'ve as well.

= -1/2 - 2

= -1/2 - 4/2

= -5/2

Quick reminder: Every lesson we learned will be helpful to the next unit and so on.

Anyways, hope everyone had a greaaat weekend!! :)