Double Angle Trigonometric Identities

Hey everyone!

For today's lesson, we studied Double Angle Trigonometric Identities which is very simple and I know that a lot of you have no troubles with it. So I'll be very brief on explaining how this one works.

Basically, this lesson is very similar to our previous lessons. The process and steps are the same.

The only thing you have to do is to find the equivalent value of the given identity from your formula sheet and substitute it to the original function.

Here are the basic Double Angle Trig Identities:

You can have different forms of equations but it will end up with the same answer as long as you don't mess up. Always choose the easier ones.

On some questions, you'll be ask to find the exact values of sin, cos or tan. Always follow the simple steps. Once you get the equation, set alpha and beta. Solve and find the value of trig identity. You need to use CAST rule, Special triangles and Pythagorean theorem to find the values depending on what you are told to look for.

As long as you know the equivalent of each set of identities(which is in our formula sheet), you'll be fine.

Hope this helps!

K bye.

Homework

Hi,Does anybody know what is the homework for today? Please reply and Thank You.

-David

Sum and Difference Part 2

Hi Guys..

Since there is no new topic and we only did exercises in the booklet... I'm just gonna answer the last question it this topic...

Hope this helps...

Sum and Difference Identities Part One

HI!!! Today in precal we studied about sum and difference identities part one.
lets go to the first example

ex. sin 7pie/12 first step that you need to do is to set an equation that will equal to 7pie/12
the equation that you need to have is either addition or subtraction. note that there is many possible equation for the example given.

sin 7pie/12=sin(4pie/12+3pie/12) *SIMPLIFY*
=sin (pie/3+pie/4) *LABEL as ALPHA and BETA*
alpha beta
at this point you have to have your formula sheet with you. The formula for this equation would be sin(A+B)= sinAcosB + cosAsinB meaning you should have sin pie/3 x cos pie/4+cos pie/3 x sin pie/4 what you have to do next is to find the exact values of these trigonometric values which means you need to use the special triangles and the cast rule. therefore you should have...





your final answer should be as stated in the image above. don't do anything to your final answer leave it as it is.

at some point you will be given csc 19pie/12. the trick to this is to solve it as sin 19pie/12 and just get the reciprocal of your final answer.

K BYE!!! ahaha...

TRIGONOMETRIC IDENTITIES

HELLO!

We started on discussing about trigonometric identities. It is basically proving that both sides of an equation are equal. To help you do this, you should always consider the following identities:

sin θ	=	1 csc θ		csc θ	=	1 sin θ
cos θ	=	1 sec θ		sec θ	=	1 cos θ
tan θ	=	1 cot θ		cot θ	=	1 tan θ

a)	sin²θ + cos²θ	=	1
b)	1 + tan²θ	=	sec²θ
c)	1 + cot²θ	=	csc ²θ

tan θ =

sin θ cos θ

cot θ =

cos θ sin θ

For example,

Answer

We express everything in terms of sin y and cos y and then simplify:

Just play around with the equation until you end up having both sides equal. BUT STILL MAKE SURE THAT YOU ARE PLAYING IT RIGHT!

More examples

Happy Birthday Mr.P

Have a Happy Birhtday!

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!! :)