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theta = arcsin(0.0138) is the principal value.

Q: How do you figure this out Sin theta equals 0.0138 so theta equals what?

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sin (theta) = [13* sin (32o)]/8 = 13*0.529919264/8 = 0.861118804 [theta] = sin-1 (0.861118804) [theta] = 59.44o

sin(0)=0 and sin(very large number) is approximately equal to that same very large number.

If sin2(theta) = 0, then theta is N pi, N being any integer

It will be a circle.

Yes, it can. If you plot theta and sin(theta) on the same graph, you will see where they intersect. I do not know of an analytical expression for this point; I think only numerical results are possible.

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If sin(theta) is 0.9, then theta is about 64 degrees or about 116 degrees.

Theta equals 0 or pi.

sin (theta) = [13* sin (32o)]/8 = 13*0.529919264/8 = 0.861118804 [theta] = sin-1 (0.861118804) [theta] = 59.44o

2 sin^2 theta = 1/4 sin^2 theta = 1/8 sin theta = sqrt(1/8) theta = arcsin(sqrt(1/8))

0.75

If sin (theta) is 3/5, then sin2 (theta) is (3/5)2, or 9/25.

sin(0)=0 and sin(very large number) is approximately equal to that same very large number.

when sin theta almost equals to theta in radians

If sin2(theta) = 0, then theta is N pi, N being any integer

It will be a circle.

2 sin (Î˜) + 1 = 0sin (Î˜) = -1/2Î˜ = 210Â°Î˜ = 330Â°

Depending on your calculator, you should have an arcsin function, which appears as sin^-1. It's usually a 2nd function of the sin key. If you don't have this function, there are many free calculators you can download... just google scientific calculator downloads.Anyway, this inverse function will give you theta when you plug in the value of sin theta. Here's the algebra written out:sin(theta)=-0.0138arcsin(sin(theta))=arcsin(-0.0138)theta=.......The inverse function applied to both sides of the equation "cancels out" the sin function and yields the value of the angle that was originally plugged into the function, in this case theta. You can use this principle to solve for theta for any of the other trig functions:arccos(cos(theta))=thetaarctan(tan(theta))=thetaand so on, but calculators usually only have these three inverse functions, so if you encounter a problem using sec, csc, or cot, you need to rewrite it as cos, sin, or tan.sec=1/coscsc=1/sincot=1/tan