SOH CAH TOA

Using inverse functions To Find Angle

\$\tan\theta = \frac{20.8}{7}\$
\$\tan^-1\theta = tan^-1(\frac{20.8}{7})\$
\$\theta = 71.4^\circ\$
Make sure calculator is in degrees to get the answer in degrees
The inverse version of sine, cosine, and tangent have the "arc" prefix

Trig Visualized

Trig Visualized

In this video d represents the line that is tangent to the circle. and the tangent also represents that slope of the radius

tangent

this works because we get the tangent with TOA or \$tan(\theta) = \frac{opposite}{adjacent}\$. We know that at a 45 degree angle \$sin(\theta)\$ and \$cos(\theta)\$ are going to be the same value. If they are divided by each other they should equal the length of the tangent/radius, which is 1. Hence, they have the same ratio.

local radii = {1, 2, 4, 5}

function toRadians(degrees)
    return (degrees * (math.pi/180))
end

for k, v in pairs(radii) do
    print(
        "radius: " ..
         v ..
         ", " ..
        "tangent: " ..
        math.tan(toRadians(45))
    )
end
output

radius: 2, tangent: 1 radius: 4, tangent: 1 radius: 5, tangent: 1

notice how the tangent is always one when you’re at a 45 degree angle. No matter what the radius.

Links