Trigonometric Identities Part 2

Today in class we continued on what we learned yesterday, verifying trigonometric identities using method one and method two. We also learned how to use conjugates and solve for θ over an interval. 

Method One: Use the fundamental identities to change one side of the equation into the same form on the other side. 

Steps:   1. State the side

            2. Do the work - change info

            3. State = other side

Method Two: use the fundamental identities to change each side  of the equation until the same form is obtained on each side. Once sides are equal state that LHS = RHS.

Example Question # 1: (method 1)
                                         

Example Question #2: (method 2)

 tan x + cot x = sec x csc x

 

 Example Question # 3:

 Solve for θ over the interval π < θ  < 2π : 

 sin²θ + 3cos²θ = 2

 1 - cos²θ + 3cos²θ = 2
  
 2cos²θ = 1 


 cos²θ = 1/2
   

            +  1
 cosθ = - √2

 cos = A/H 

 Quad 1 = 0 + π/4 = π/4  (not within interval)

 Quad 2 = π - π / 4 = 3π/4  (not within interval)

 Quad 3 = π + π/4 = 5π/4
 Quad 4= 2π - π/4 = 7π/4 


  θ = 5π/4, 7π/4

Here are some videos I found that are helpful if you still aren't understanding verifying identities:


This video has multiple examples and many tips to help you.
Video # 1 
This video has only one example but has a more detailed explanation of how to solve the problem.
Video # 2 

Homework for today was: 
Exercise 14, Questions 1-20, Omit 11a
Exercise 15, Questions 1-20, #12 solve algebraically
Trigonometric Identities Worksheet, 7-13