SOLUTION: How do you find the solutions of the equation sin2x + cos(x)=0

Algebra.Com
Question 172849This question is from textbook
: How do you find the solutions of the equation sin2x + cos(x)=0 This question is from textbook

Found 2 solutions by solver91311, Alan3354:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!
Your problem statement is ambiguous. Do you mean or ?
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
sin2x + cos(x)=0
=============
sin^2 = 1-cos^2
1-cos^2 + cos = 0
cos^2 - cos - 1 = 0
A quadratic in cos(x)
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=5 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.61803398874989, -0.618033988749895. Here's your graph:

cos(x) = 1/2 + sqrt(5)/2 =~1.618
cos>1 is not a real number, so ignore it.
-------------------
cos(x) = 1/2 - sqrt(5)/2 =~ -0.618
x = 128.173º





RELATED QUESTIONS

Find all values of x in the interval [0, 2π] that satisfy the given equation.... (answered by DrBeeee)
Find all solutions to the equation. sin2x + sin x =... (answered by Alan3354)
Find all solutions to the equation. sin2x + sin x =... (answered by solver91311)
Find all the solutions in the interval [0, 2pi): sin2x = cos... (answered by stanbon)
Rewrite the equation {{{ sin2x=cos(x) }}} using only cos(x) (and numbers). Then find all (answered by Alan3354)
Find all solutions of the equation in the interval [0, 2 pi) -sin2x+2cosx=0 (answered by ikleyn)
Find solutions in the internal (0,2π) Cos^2x+2cosx+1= 0... (answered by ikleyn)
Find all solutions of each of the equations in the interval [0,2pi). a)... (answered by KMST)
Find all solutions of each equation in the interval [0,2Ï€) cos(x) + cos (3x) =... (answered by ikleyn)