You cannot prove it because it is not true!
cos(0) = 1
cos(2*pi) = 1
cos(4*pi) = 1
...
cos(2*k*pi) = 1 for all integers k
or, if you still work in degrees,
cos(0) = 1
cos(360) = 1
cos(720) = 1
...
cos(k*360) = 1 for all integers k
theta = arcsin(0.0138) is the principal value.
(in a past paper it asks u to solve this for -180</=theta<180, so I have solved it) Tan theta =-1, so theta = -45. Use CAST diagram to find other values of theta for -180</=theta<180: Theta (in terms of tan) = -ve, other value is in either S or C. But because of boundaries value can only be in S. So other value= 180-45=135. Do the same for sin. Sin theta=2/5 so theta=23.6 CAST diagram, other value in S because theta (in terms of sin)=+ve. So other value=180-23.6=156.4.
tan (theta x theta) : must square the value of the angle, theta, before applying the trig function, tangent.
To apply the transformation ( w = z + \frac{1}{z} ) to the circle defined by ( |z| = 2 ), we can express ( z ) in polar form as ( z = 2e^{i\theta} ), where ( \theta ) ranges from ( 0 ) to ( 2\pi ). Substituting this into the equation for ( w ), we get ( w = 2e^{i\theta} + \frac{1}{2e^{i\theta}} = 2e^{i\theta} + \frac{1}{2} e^{-i\theta} ). This simplifies to ( w = 2e^{i\theta} + \frac{1}{2}(\cos \theta - i \sin \theta) ), which describes a new curve in the ( w )-plane. The resulting curve can be analyzed further to understand its geometric properties.
Any value for which sin(theta) = 0, i.e. theta = N*180, N being an Integer.
theta = arcsin(0.0138) is the principal value.
0.75
(in a past paper it asks u to solve this for -180</=theta<180, so I have solved it) Tan theta =-1, so theta = -45. Use CAST diagram to find other values of theta for -180</=theta<180: Theta (in terms of tan) = -ve, other value is in either S or C. But because of boundaries value can only be in S. So other value= 180-45=135. Do the same for sin. Sin theta=2/5 so theta=23.6 CAST diagram, other value in S because theta (in terms of sin)=+ve. So other value=180-23.6=156.4.
-0.5736
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
tan (theta x theta) : must square the value of the angle, theta, before applying the trig function, tangent.
True
That depends on the value of the angle, theta. csc is short for "cosecans", and is the reciprocal of the sine. That is, csc theta = 1 / sin theta.
No, they cannot all be negative and retain the same value for theta, as is shown with the four quadrants and their trigonemtric properties. For example, in the first quadrant (0
Your question is insufficiently precise, but I'll try to answer anyway. "Sine squared theta" usually means "the value of the sine of theta, quantity squared". "Sine theta squared" usually means "the value of the sine of the quantity theta*theta". The two are not at all the same.
Any value for which sin(theta) = 0, i.e. theta = N*180, N being an Integer.
You can use the Pythagorean identity to solve this:(sin theta) squared + (cos theta) squared = 1.