Question

Find expressions for the derivatives of csc x, sec x, and cot x by first using
identities to write them in terms of sine or cosine or both

Answer 1

By definition, sec(x)=1/cos(x); csc(x)=1/sin(x) and cot(x) = cos(x)/sin(x). Using known formulas of cos and sin derrivatives and quotient derrivatives rule:(f(x)/g(x))'=(f(x)'g(x)-g(x)'f(x))/(g(x)^2) you will solve your problem.

Answer 2

ohh I think I got it thanks :)
could you also explain and help me make sense of this please?

Answer 3

Well, at first you should know that \[\frac{ \pi }{ 180 }\] is equal to 1. Then 2 and 3 are derivative formulas, and 1 is well known fact (you can find the proof e.g. in http://math.ucsd.edu/~wgarner/math20a/sin(x)_over_x.htm)

Answer 4

How does pi/180 equal 1?
And the link doesn't seem to work.

Answer 5

One radian is equal to 180/pi degrees. So, pi/180 = 180/pi (rad). For the link, you should erase the bracket, written by mistake: http://math.ucsd.edu/~wgarner/math20a/sin(x)_over_x.htm

Answer 6

Thank you so much! :)