SOLUTION: Solve the equation https://gyazo.com/9c9598aa5e71b13cfbae900cfcb97636 (equation picture link) where 0≤x≤2π

Algebra.Com
Question 1205297: Solve the equation https://gyazo.com/9c9598aa5e71b13cfbae900cfcb97636 (equation picture link) where 0≤x≤2π
Found 3 solutions by MathLover1, ikleyn, Alan3354:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

....both sides multiply by

...replace with
...factor


solutions:
=>
=>
replace with



=>
=>

solutions in given interval :
=>°
=>°
=>°


Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
- - = 0.     Solve for   0 <= x < .
~~~~~~~~~~~~~~~~~~~~~~ 

Multiply both sides of the given equation by 2.  

You will get an equivalent equation

     = 0.


Factor left side

    (2sin(x)+1) * (sin(x)-1) = 0.


Case 1.  2sin(x) + 1 = 0  --->  sin(x) =   --->  x =   or  x = .


Case 2.   sin(x) - 1 = 0  --->  sin(x) = 1  --->  x = .


ANSWER.  The set of solutions is  ,    and  ,  in ascending order.

Solved.



Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Solve the equation https://gyazo.com/9c9598aa5e71b13cfbae900cfcb97636 (equation picture link) where 0≤x≤2π
----------------

Sub x for sin(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=2.25 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1, -0.5. Here's your graph:

========================
sin(x) = 1
x = 90 degs or pi/2
----
sin(x) = -0.5
x = 210 degs or 7pi/6
x = 330 degs or 11pi/6
RELATED QUESTIONS

Solve the equation cos2x + sin^2x = 4/9 to the nearest hundredth where 0 ≤ x ≤ 2π.... (answered by MathLover1)
Solve log8(log5x) = 0. equation orientation:... (answered by MathLover1,Theo,MathTherapy,greenestamps)
Determine the exact value of cos19π/12. Link to equation composition:... (answered by ikleyn)
Prove that csc2x = 1/2 secx cscx. Link to the composition of the equation:... (answered by MathLover1)
solve 2^4x = 1/32 for x. equation orientation:... (answered by Theo,ikleyn,math_tutor2020)
Prove that 2sec^2x-2tan^2x/cscx = sin2x secx Link to equation composition:... (answered by MathLover1)
Solve log2 x-log2 6=log2 5+2log2 3 for x. equation orientation:... (answered by MathLover1,josgarithmetic)
Describe the transformations that take the graph of f(x)=log4 x to the graph of g(x) =... (answered by greenestamps)
Describe the transformations that take the graph of f(x)=log4 x to the graph of g(x) =... (answered by MathLover1)