Trigonometry

1. Basics

1.2 Formulas

• sin(x)=opposite/hypothenuse
• cos(x)=adjacent/hypothenuse
• tan(x)=opposite/hypothenuse(=sin(x)/cos(x))


• sin(x)=-sin(-x)
• cos(x)=cos(-x)
• tan(x)=-tan(-x)


• (sin(x))^2+(cos(x))^2=1
• (tan(x))^2+1=1/(cos(x))^2
• 1/(tan(x))^2+1=1/(sin(x))^2


• sin(x+y)=sin(x)cos(y)+cos(x)sin(y)
• cos(x+y)=cos(x)cos(y)-sin(x)sin(y)
• tan(x+y)=(tan(x)+tan(y))/(1-tan(x)tan(y))


• sin(x)+sin(y)=2sin((x+y)/2)cos((x-y)/2)
• sin(x)-sin(y)=2sin((x-y)/2)cos((x+y)/2)
• cos(x)+cos(y)=2cos((x+y)/2)cos((x-y)/2)
• cos(x)-cos(y)=-2sin((x+y)/2)sin((x-y)/2)


• sin(x)+sin(y)+sin(z)+sin(x+y+z)=4sin((x+y)/2)sin((y+z)/2)sin((x+z)/2)
• cos(x)+cos(y)+cos(z)-cos(x+y+z)=4cos((x+y)/2)cos((y+z)/2)cos((x+z)/2)
• tan(x)+tan(y)+tan(z)+tan(x+y+z)=4