theta = arcsin(0.0138) is the principal value.
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.
The expression "cot theta = 1.5 sin theta" can be rewritten using the definitions of trigonometric functions. Since cotangent is the reciprocal of tangent, we have cot(theta) = cos(theta) / sin(theta). Therefore, the equation becomes cos(theta) / sin(theta) = 1.5 sin(theta), leading to cos(theta) = 1.5 sin^2(theta). This relationship can be used to find specific values of theta that satisfy the equation.
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.
If sin(theta) is 0.9, then theta is about 64 degrees or about 116 degrees.
If sin2(theta) = 0, then theta is N pi, N being any integer
It will be a circle.
2 sin (Θ) + 1 = 0sin (Θ) = -1/2Θ = 210°Θ = 330°
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
you have to do the arcsin which is sin-1 on your calculator. i have not met anyone in my life who can do sin or arcsin in their head. not even my college teachers. your theta is equal to 20degrees