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- MIT grad shows how to find sin, cos, and tan using SohCahToa as well as the csc, sec, and cot trig functions.
If you have a right triangle with side lengths given and an angle (theta), you can easily find the sine, cosine, and tangent trig functions. Remember that the longest side of the triangle is the 'HYPOTENUSE', the side directly opposite theta is the 'OPPOSITE', and the other side next to theta is the 'ADJACENT' side.
Once you've identified the hypotenuse (H), adjacent (A), and opposite sides (O), you can find Sin, Cos, and Tan:
Sin of theta = Opposite over Hypotenuse (SOH)
Cos of theta = Adjacent over Hypotenuse (CAH)
Tan of theta = Opposite over Adjacent (TOA)
The mnemonic SOH CAH TOA can help you remember which sides to use for sin, cos, and tan. For instance, SOH stands for Sin = Opposite over Hypotenuse
If you need to find one of the other three trig functions (Csc, Sec, or Cot), the easiest way to find them is to first find Sin, Cos, or Tan and then take the reciprocal (or flip) the fraction, since:
Csc = 1 / Sin
Sec = 1 / Cos
Cot = 1 / Tan
For example, if you find that Cos of an angle is equal to 3/5, the Sec of that angle would be equal to 5/3.