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Consider the function siny
We could make a graph of the slope: slope
1
0
1
0
1Now we connect the dots!
The resulting curve is a cosine curve.
sin cosd
x xdx
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We can do the same thing for cosy slope
0
1
0
1
0The resulting curve is a sine curve that has been reflected about the x-axis.
cos sind
x xdx
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We can find the derivative of tangent x by using the quotient rule.
tand
xdx
sin
cos
d x
dx x
2
cos cos sin sin
cos
x x x x
x
2 2
2
cos sin
cos
x x
x
2
1
cos x
2sec x
2tan secd
x xdx
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Derivatives of the remaining trig functions can be determined the same way.
sin cosd
x xdx
cos sind
x xdx
2tan secd
x xdx
2cot cscd
x xdx
sec sec tand
x x xdx
csc csc cotd
x x xdx
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