Christmas Wishes

Merry Christmas and a Happy New Year to everyone.

Mr.P

Hi Everyone,

I hope everything is going well, and you are learning/getting ready for the exam.
If I get some time I will post couple pictures (perhaps selfies).
Keep up the good work.
Until next type.
From Lousika/Patras, Greece, Europe, World.

Mr. P

Trig Help

Hello there Fellow classmates, Irene here. You all probably know me. Im tiny, but hard to miss. Im not going to make this message long and get to the point. I am posting this because I want to help everybody. The last trig test didn't as I planned. :( After that I was determined to get a better grade. I wanted to get more practice, to be more prepared for the next precal test. So I decided to go to the old precal exams and copy every single question that had the word sin, cos, tan, csc, sec, cot, and everything that relates to trig. I started from June 2013 and went all the way back to January of 2007. I wanted to go all the way to 2004, but sadly I got busy with other things and ran out of time. I hope you will make good use of my endless hours of coping and pasting.

PS I didn't get any questions from booklet one of January 2007 because it was malfunctioning :(


Here's the link
https://www.dropbox.com/s/p9x4m3q0ntwey90/trig%20unit.docx

Hi! Everyone, My name is Shivani. You probably know me, but if you don't I sit right in middle of Harsimran and Ruthanne. Now I shall introduce you with Solving Trigonometric Equations using Identities.


Trignometric Identities are equations involving the trignometric function that are true for every values of the variables involved. Youn can use trignometric identites along with algebric methods to solve trignometric equations.

Example
Find all the solutions of the equation in the interval 2sin²x=2+cosx

The equation contains both sine and cosine functions.
We rewrite the equation so that it contains only cosine functions using the Pythagorean Identity sin²x=1cos²x

Factoring cosx, we get,cosx(2cosx+1)=0

By using zero-product-property,we will get cosx=0,and 2cosx+1=0 whcih yields x= ^-1⁄₂
In the interval [0, 2π), we know that cosx=0 when x=^π⁄₂ and x= ^3π⁄₂ .On the other hand, we also know that cosx= ^-1⁄₂ when x= ^2π⁄₃ and x= ^4π⁄₃
Therefore, the solutions of the given equation in the interval [0, 2π) are { ^π⁄₂,^3π⁄₂,^2π⁄₃,^4π⁄₃}

I hope you've learned something ! And
Good luck for the test. :)