3.5 Derivatives of Trig Functions London Bridge, Lake Havasu City, Arizona Photo by Vickie Kelly, 2001 Greg Kelly, Hanford High School, Richland, Washington Consider the function y sin slope We could make a graph of the slope: 2 1 0 1 Now we connect the dots! 0 2 The resulting curve is a cosine curve. 1 0 d sin x cos x dx We can do the same thing for y cos slope The resulting curve is a sine curve that has been reflected about the x-axis. 2 0 2 0 1 0 1 0 d cos x sin x dx We can find the derivative of tangent x by using the quotient rule. d tan x dx cos 2 x sin 2 x cos 2 x d sin x dx cos x 1 cos 2 x cos x cos x sin x sin x sec 2 x cos 2 x d tan x sec2 x dx Derivatives of the remaining trig functions can be determined the same way. d sin x cos x dx d cot x csc 2 x dx d cos x sin x dx d sec x sec x tan x dx d tan x sec 2 x dx d csc x csc x cot x dx