Expert: Paul Klarreich - 12/23/2007

Question
Hey Paul thanks for the help earlier. I have another one that is giving me a hard time. The problem is: Solve

4cosx + 3 = 0 [0,2pi) rounding your answers to three decimal places

my problem is the quadratic formula uses three numbers:

What three numbers do i use. From what I can tll I don't have an "A" number which means I cant use the quadratic formula which it asks me to do. Thanks for all your help. Take Trig online is not as smart an idea as i thought. LOL

Thanks again

Answer
Questioner:   Harmon
Category:  Advanced Math
Private:  No
 
Subject:  Solving Trigonometric Equations Using the Quadratic Formula
Question:  Hey Paul thanks for the help earlier. I have another one that is giving me a hard time. The problem is: Solve

4cosx + 3 = 0 [0,2pi) rounding your answers to three decimal places

my problem is the quadratic formula uses three numbers:

What three numbers do i use. From what I can tll I don't have an "A" number which means I cant use the quadratic formula which it asks me to do. Thanks for all your help. Take Trig online is not as smart an idea as i thought. LOL

>> Are you actually paying them for it?  Then THEY should answer your questions.  Let them earn their fees.


Thanks again
...........................................
Hi, Harmon,

No, your problem is that this is not a quadratic equation.  Use this 'abbreviation trick':

Write C for cos x, just temporarily.  Now your equation is:

4C + 3 = 0, not a quadratic at all.  Solve:

4C = - 3,

C = -3/4.

Now 'disabbreviate':  {OK,OK, so I made up that word.]

cos x = -3/4

Now you want  x = arccos(-3/4)  and you use the calculator.  On my Windows calc, you press:

[Be sure to check the Radians button.]
3
/
4
=
+-  [now you have -0.75]
Inv
cos

and you have x = 2.4188584057763776272842660306382, which rounds to
2.419 radians