Sure, let's find the values of these trigonometric functions one by one.
We will use degrees to radians conversion, where 1 degree equals π/180 radians, for those trigonometric functions which are given in degrees and since trigonometric functions in Python use radians.
1. sin 765^0
Firstly, we need to convert 765 degrees into radians.
765 * (π/180) gives us the radian. Then to calculate the sine of this radian value, we end up with a result of approximately 0.7071067811865478.
2. csc (−1410^0)
To find the cosecant of −1410 degrees, first, convert the angular value to radians by multiplying −1410 by (π/180).
Cosecant is the reciprocal of the sine function. Hence, the cosecant of our radian value represents the reciprocal of the sine of that value. So, after calculating, we get approximately 1.9999999999999987.
3. tan 19π/3
Here the angular value is already given in radians, so we can directly find the tangent. The resulting value for tan(19π/3) turns out to be approximately 1.7320508075688694.
4. sin (−11π/3)
For the sine function, the angle is already in radians. We directly find the sine of (−11π/3), and the output results in approximately 0.8660254037844392.
5. cot(−15π/4)
The cotangent function is the reciprocal of the tangent function, so we find the cotangent of (−15π/4) by taking the reciprocal of the tangent value of the same angle. After finding our result, we get approximately 0.9999999999999973.
So, the list of results for these trigonometric functions are as follows:
sin 765^0 = 0.7071067811865478
csc (−1410^0) = 1.9999999999999987
tan 19π/3 = 1.7320508075688694
sin(−11π/3) = 0.8660254037844392
cot(−15π/4) = 0.9999999999999973