Trigonometry Tricks 3

tan(90° - x) = ctn x

ctn(90° - x) = tan x

Examples:

tan 60° = 1.7320508...

ctn 30° = 1.7320508...

tan 75° = 3.7320508...

ctn 15° = 3.7320508...

ctn 45° = 1

tan 45° = 1

(Notice that the tangent & cotangent of 45 degrees are exactly the same!) Plus, they're the only rational examples here! By the way, 1.7320508... = the square root of 3; tan 75° & ctn 15° are both equal to 2 plus the square root of 3.

The tangent & cotangent functions are reciprocals of each other, so:
tan X = 1/ctn X & ctn X = 1/tan X.

Just one more thing I have to tell you: the tangent of 90 degrees is undefined, so the cotangent of 0 degrees is also undefined! However, the tangent of 0 degrees is simply equal to 0, but the cotangent of 90 degrees is also undefined! Weird, huh?

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