/sci/ - Science & Math

>>11270159
unit circle and the right triangles with sides 1-1-√2 and 1-√3-2.

You can deduce stuff like sin(atan(x))=x/√(1+x^2) by considering a right triangle of sides 1 and x, and there's also a diagram to find cos(x+y)=cos(x)cos(y)-sin(x)sin(y).

You can find these on wikipedia at List of trigonometric identities

>>7547427
Well, actually 30 minutes is pretty optimistic and only the case if you are teaching them to one person who has already struggled with trig. Still it should be doable in a few hours.

This will help with identities.

>>7044250
pic related verses:

Let the unit vector in the x axis (1, 0) be
⌈1⌉
⌊0⌋
and the unit (basis) vector in the y direction be
⌈0⌉
⌊1⌋
Then the matrix A(ϕ) that rotates (counter clockwise) a vector by ϕ will take the unit vector in x direction to
⌈cos(ϕ)⌉
⌊sin (ϕ)⌋
and takes the y vector to
⌈-sin(ϕ)⌉
⌊cos(ϕ)⌋
Thus A(ϕ) equals
⌈cos(ϕ) -sin(ϕ)⌉
⌊sin (ϕ) cos(ϕ)⌋
Hence the unit vector at θ to the x axis will be rotated to θ+ϕ after applying A(ϕ)
⌈cos(ϕ+θ)⌉=⌈cos(ϕ) -sin(ϕ)⌉*⌈cos(θ)⌉
⌊sin (ϕ+θ)⌋=⌊sin (ϕ) cos(ϕ)⌋*⌊sin (θ)⌋