SOLUTION: solve the equation for solutions in the interval from [0,360 degrees): sin(2 theta) +1=cos(2 theta)

Question 918939: solve the equation for solutions in the interval from [0,360 degrees): sin(2 theta) +1=cos(2 theta)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
solve the equation for solutions in the interval from [0,360 degrees): sin(2 theta) +1=cos(2 theta)
-------
sin + 1 = cos = 1 - sin^2
sin^2 + sin - 1 = 0
x = sin(2theta)
x^2 + x - 1 = 0
---

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: 0.618033988749895, -1.61803398874989. Here's your graph:

============
x =~ 0.618034 = 2theta
2theta =~ 38.17, 321.83, 398.18, 681.83 degs
theta = 19.085, 160.91, 199.09, 340.91 degs

RELATED QUESTIONS
solve the equation for solutions over the interval [0 degrees, 360 degrees). 2 sin... (answered by lwsshak3)

solve equation for solutions over the interval (0 deg, 360 deg) cos^2 theta = sin^2... (answered by Alan3354)

Solve the equation sin(theta)+cos(theta)= 2(sin(theta)- cos(theta)), for 0 (answered by lwsshak3,KMST)
Solve the equation in the interval (0 degrees, 360 degrees) sin^2 theta-sin... (answered by ikleyn,greenestamps)
Solve the equation for solutions over the interval [0, 360). Give solutions to the... (answered by jim_thompson5910)
find two solutions in the interval 0 degrees (answered by Fombitz)
solve algebraically for all values of theta in the interval 0-360 that satisfy the... (answered by lwsshak3)
Solve for theta 0 degrees < theta < 360 degrees.... (answered by solver91311,lwsshak3)
solve the equation for solutions in the interval from [0,360 degrees): 4 cos squared... (answered by Alan3354)