Must Know Trig for Calc II (Math 151)

Calculus Trig Identities for Math 151

sin²(x) + cos²(x) =

1

tan²(x) + 1 =

sec²(x)

1 + cot²(x) =

csc²(x)

cos²(x) = (Half Angle)

[1 + cos(2x)]/2

sin²(x) = (Half Angle)

[1 - cos(2x)]/2

sin(2x) = (Double Angle)

2sin(x)cos(x)

cos(2x) = (Double Angle)

cos²(x) - sin²(x)

d/dx [sin(x)]

cos(x)

d/dx [cos(x)]

-sin(x)

d/dx [tan(x)]

sec²(x)

d/dx [cot(x)]

csc²(x)

d/dx [sec(x)]

sec(x)tan(x)

d/dx [csc(x)]

-csc(x)cot(x)

∫ [sin(x)] dx

-cos(x) + c

∫ [cos(x)] dx

sin(x) + c

∫ [sec(x)] dx

ln |sec(x) + tax(x)| + c

∫ [tan(x)] dx

ln |sec(x)| + c OR -ln |cos(x)| + c

∫ [cot(x)] dx

ln |sin(x)| + c

∫ [csc(x)] dx

ln |csc(x) - cot(x)| + c

∫ [csc²(x)] dx

-cot(x) + c

Formula for the disk method

V = π ∫ₐᵇ [f(x)]² dx

Formula for Cylindrical Shell Method

V = 2π ∫ₐᵇ [x(f(x))] dx