Trig functions Calc

Sin²x+Cos²x

=1

1 + tan²x

=sec²x

cot²x+1

=csc²x

sin2x

=2sinxcosx

Sinx + cosx

=1/2 sin(2x)

cos2x

=cos²x-sin²x

sin²x

=(1-cos2x)/2

cos²x

=(1+cos2x)/2

√(a²-x²)

x = asinΘ
cos²Θ=1-sin²Θ

√(a²+x²)

x=atanΘ
sec²Θ=1+tan²Θ

√(x²-a²)

x=asecΘ
tan²Θ=sec²Θ-1

∫sinudu

= -cosu + C

∫cosudu

= sin u + C

∫tanudu

= -ln|cosu| + C

∫cscudu

= -ln|cscu + cotu| + C

∫secudu

= ln|secu + tanu| + C

∫cotudu

= ln|sinu| + C

∫e^u du

= e^u + C

∫1/u du

= ln|u| + C

∫a^u du

= (a^u)/lna + C

∫1/(1+x²)dx

= arctanx + C

∫1/√(1-x²)dx

= arcsinx + C

∫-1/√(1-x²)dx

= arccosx + C

∫1/(a²+u²)du

= 1/a(arctan(u/a)) + C

∫1/√(a²-u²)du

= arcsin(u/a) + C

∫1/(u√(u²-a²))

= 1/a(arcsec(|u|/a) + C