Question 1139358: What are the solutions from 0 to 360 degrees?
Solve the following. Find all solutions from 0 degrees to 360 degrees.
1. 2 sin^2 x + 7 sin x = 4
2. cos x sin x + sin x = 0
3. 2 sin^2 x - 1 = 0
Answer by rapture1965(18)   (Show Source):
You can put this solution on YOUR website! I will solve number 3 only. Post one question at a time. By doing so, it will encourage others to help you. Posting many questions without showing math work pretty much reveals your lack of interest in terms of learning the material. Understand?
We have the following trigonometric equation: 2sin^2 x - 1 = 0
Let u = sin x for easy calculation. In fact, any letter can be used as a temporary substitute for the trig expression.
2u^2 - 1 = 0
Solve for u.
2u^2 = 1
u^2 = 1/2
sqrt{u^2} = sqrt{1/2}
u = sqrt{2}/2
Back-substitute for u. In other words, replace u with sin x.
sin x = sqrt{2}/2.
According to the unit circle, we know the point (cos x, sinx) lies on the circle. Use the unit circle to find all sin x from 0 degrees to 360 degrees that represent the value sqrt{2}/2.
Below are all solutions from 0° to 360°.
In Radians:
pi/4, 7pi/4, 5pi/4, 3pi/4
In Degrees:
45°, 315°, 225°, 135°
I hope this helps.
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