How to tell when to use sin, cos or tan

Step-by-step explanation:

Keep in mind that these three trig functions can be interpreted as being the ratios of the side lengths of a triangle:

            opposite side

sin x =

              hypotenuse

            adjacent side

cos x =

              hypotenuse

            opposite side

tan x =

             adjacent side

In the case where you have a right triangle and know the lengths of two of its three sides, that knowledge dictates which of the above trig functions to use in "solving the triangle."

If, for example, the "opposite side" of a triangle is 3 and the "hypotenuse" is 5, we'd choose to use the sine function to find the angle opposite the "opposite side:"

            opposite side       3 units

sin x = =

              hypotenuse         5 units

Find x by using the inverse sine function:

Angle x = arcsin 3/5 = 0.644 radians or 36.9 degrees.

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