SOLUTION: Use the t-method to solve sin(x) + 2 cos(x) =sqrt5/2 (leave answers correct to three decimal places): i) On the domain 0°≤θ≤180° ii) On the domain π≤θ≤2π

Algebra ->  Trigonometry-basics -> SOLUTION: Use the t-method to solve sin(x) + 2 cos(x) =sqrt5/2 (leave answers correct to three decimal places): i) On the domain 0°≤θ≤180° ii) On the domain π≤θ≤2π       Log On


   

Question 1203996: Use the t-method to solve sin(x) + 2 cos(x) =sqrt5/2 (leave answers correct to three decimal places):

i) On the domain 0°≤θ≤180°

ii) On the domain π≤θ≤2π

iii) On the domain -3π≤θ≤3π
I am struggling to get through this question and its possibly harder than I think it is. Hoping for your help.
Found 2 solutions by Solver92311, math_tutor2020:
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


Let

then and

so



Multiply by

Simplify to standard quadratic form and solve for on the low half of the given domain. Use a calculator to find , then multiply by 2.


John

My calculator said it, I believe it, that settles it

From
I > Ø

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

This video shows how the t-formula is derived
https://www.youtube.com/watch?v=jsAVMhmsFco

And this video shows why the formula is useful to solving trig equations
https://www.youtube.com/watch?v=6_QqFUwKwyk

Hopefully those are enough to get you started. If not then please let me know.