Basic Trigonometry: Sin Cos Tan (NancyPi)

MIT grad shows how to find sin, cos, and tan using SohCahToa as well as the csc, sec, and cot trig functions. To skip ahead: 1) For how to find the adjacent, opposite, and hypotenuse sides of the right triangle, skip to 1:13. 2) For how to find the value of SIN of theta using SOH CAH TOA, skip to 3:16. 3) For how to find COS, skip to 4:15. 4) For how to find TAN, skip to 4:56. 5) For how to find CSC, SEC, AND COT from the sin, cos, and tan functions, skip to 5:56. 6) For harder examples of how to label the adj, opp, and hyp sides if the TRIANGLE IS ROTATED on its side or upside down, skip to 8:32. Nancy formerly of MathBFF explains trigonometry basics.

For MORE TRIG: how to convert between radians and degrees, jump to: https://youtu.be/l6hSY2Pcch0

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SIN COS TAN: If you have a right triangle with side lengths given and an angle (theta), you can easily find the sine, cosine, and tangent trigonometric 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 using these trigonometric ratios:

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 the sine, cosine, and tangent trig ratios. For instance, SOH stands for Sin = Opposite over Hypotenuse

CSC SEC COT: If you need to find one of the other three trig functions (cosecant, secant, or cotangent), 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.

For more of my mathematics videos, check out: http://nancypi.com