Find the six trigonometric ratios of the angle in the following diagram:

Solution:

sinO = __opposite sin = . ____________ sin0 = __hypotenuse sin.. =__2/3			csc0 = __hypotenuse csc = . ____________ csc0 = __opposite csc.. =__3/2
cos0 = __adjacent cos = . ____________ cos0 = __hypotenuse cos.. =__/3			sec0 = __hypotenuse sec = . ____________ sec0 = __adjacent sec.. =__3/
tanO = __opposite tan = . ____________ tan0 = __adjacent tan.. =__2/			cot0 = __adjacent cot = . ____________ cot0 = __opposite csc.. =__/2

Example 2:

If cos = 3/4, find the other five trigonometric ratios of .

Solution:

Since cos is defined as the ratio of the adjacent side to the hypotenuse, we drow a triangle with hypotenuse of length 4 and a side of length 3 adjacent to . We use the Pythagorean Theorem to find the opposite side. Let it be x for now. Then we get:

3² + x² = 4²
Therefore:
x² = 7 so x =

Hence the triangle looks like:

________

So the other trig ratios are as follows:

sin = /4		csc = 4/
	sec = 4/3
tan = /3		cot = 3/

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