trig derivatives, integrals, and identities

pythagorean identities

cos² + sin² = 1

1 + tan² = sec²

cot² + 1 = csc²

sin double angle

2 cos sin

cos double angle

cos² - sin²

1 - 2sin²

2cos² - 1

cos double angle solved for cos²

½ times 1 + cos2x

cos double angle solved for sin²

½ times 1 - cos2x

derivatives of all trig functions

integrals of all trig functions

derivatives of all inverse trig functions

what is the integral of lnx

xlnx-x+C

things to remember

• DON’T FORGET DX, +C, AND TRIG IDENTITIES

• heaviside always works as long as it’s distinct

• the integral of lnx is xlnx-x+c

• you can integrate double angle but not trig squared (other than cos and sin)

• if it gives you a rate and how many people infected, you can plug stuff back into og dy/dx equation to solve for K

• remember the ln ends up being a fraction because one of them, the variable is negative so you have to subtract that ln not add

• if you have to find the maximum rate of infection, set original dy/dx equation equal to 0

• remember chain rule for inverse trig (numerator is usually not 1, but another integer)

• remember ln isn’t always the end goal

• factor out quadratic for odd/even trig

• remember to use ln|x| not ln(x)

• if you have y - a over y - b and want y by itself, you have to multiply both sides by denominator then factor it out then combine like terms to one side then factor again and divide

• for sec of odd power you have to use u and du and get to a point where you have same integral with dif coefficient by using trig sub

• only reassociate if you have to, like if there’s lnx, don’t do it for small polynomials just take the long way