SOLUTION: Hello. I have the following trigonometric question to answer but im stuck. Please note the B in the equation is Beta. Solve the following for between 0 and 360 degrees: {{{ (1+4 si

Click here to see ALL problems on Trigonometry-basics

Question 719291: Hello. I have the following trigonometric question to answer but im stuck. Please note the B in the equation is Beta. Solve the following for between 0 and 360 degrees: .
I have done the following: 3-2sinB + 12sinB - 8sin^2B = 2, which then goes to -8sin^2B + 10sinB +1 = 0

Is my next step to transform this into a quadratic equation? and then work out both sections individually as equalling zero?
Any advice would be great. Thanks!
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Solve the following for B between 0 and 360 degrees:
(1+4 sin B)(3-2 sin B)=2
-----
Let x = sin(B)
-----
(1+4x)(3-2x) = 2
3 + 10x - 8x^2 = 2
---
8x^2 -10x - 1 = 0
-----
x = [10 +- sqrt(100-4*8*-1)]/16
----
x = [10 +- sqrt(132)]/16
----
Usable solution:
x = -0.0931
-----
Solve for "B"
sin(B) = -0.0931
B = sin^-1(-0.0931) = 354.66 degrees or B = 185.34 degrees
=============================================================
Cheers,
Stan H.
==================

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

That is exactly what you need to do. The ugly thing doesn't factor either. So without using your calculator to get approximations of the values, the best you will be able to do is report that .

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it