sin theta - 2sin^2 theta = 0
I'm using the up carrot sign to signal "to the power of..."
Let sin theta = x
x - 2 x^2 = 0
x (1 - 2x) = 0
Both x=0 and x = 1/2 are solutions.
theta = 0 degrees, 30 degrees, 150 degrees and 180 degrees.
Thank you so much!!! im a little confused on how you got the degrees though. I know that is what you are supposed to end up with but i cant connect how you go from the solution to the degrees. could you please explain?
if x= sintheta=0
then theta= arc sin 0
On your calculator, this may be the inv sin or sin-1 key
oh right! thank you so much!
You're welcome! I'm glad I could help clarify that for you. To explain further, when solving trigonometric equations like sin(theta) - 2sin^2(theta) = 0, we usually represent the unknown angle theta as x for simplicity. We solve the equation by factoring out x, which gives us x(1 - 2x) = 0.
Now, to find the values of x that satisfy this equation, we set each factor equal to zero and solve for x. So we have x = 0 and 1 - 2x = 0, which simplifies to x = 1/2.
Since we initially represented x as sin(theta), we replace x with sin(theta) in the solutions we found. Therefore, the two possible values for sin(theta) are 0 and 1/2.
To find the corresponding angles in degrees, we use the inverse sine function (arcsin or sin^-1) on these values. In the case of sin(theta) = 0, we have theta = arcsin(0) = 0°, since the sine of 0° is 0.
Similarly, for sin(theta) = 1/2, we have theta = arcsin(1/2) = 30°. This is because arcsin(1/2) is the angle whose sine is 1/2, and that angle is 30°.
Since the sine function is periodic, it repeats every 180°, adding k * 180° to each of our solutions, where k is an integer. Therefore, the additional solutions are theta = 30° + 180° = 210°, and theta = 180° - 30° = 150°.
Hence, the solutions for theta in degrees are 0°, 30°, 150°, and 180°.