What actually are sine, cosine, and tangent? Are they numbers that go on infinitely, like pi? 
+128731 What actually are sine, cosine, and tangent? Are they numbers that go on infinitely, like pi?
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They are ratios......specifically - in right triangles - of one of the side lengths to the hypoteneuse or of one of the "legs" to the other. If we're looking at some angle in a right triangle other than the right angle, the sine is the ratio of the "leg" opposite that angle to the hypoteneuse length. The cosine is the ratio of the length of the "leg" adjacent to that angle to the hypoteneuse length. The tangent is the ratio of the length of the opposite "leg" to the adjacent "leg."
The normal sine and cosine functions have"ranges" between -1 and , inclusive. So they take on all real number values in this range......Thus, their values can be either "irrational"(non-repeating decimals like the "decimal" part of pi), or "rational" (can be expressed as a fraction) in this range, depending on the angle.
The tangent, (where defined), has a range from -∞ to +∞. It takes on all real number values - rational and irrational. Note, that for reasons I won't go into, the tangent isn't defined for certain angles!!
Hope that helps 
+128731 What actually are sine, cosine, and tangent? Are they numbers that go on infinitely, like pi?
-----------------------------------------------------------------------------------------------------
They are ratios......specifically - in right triangles - of one of the side lengths to the hypoteneuse or of one of the "legs" to the other. If we're looking at some angle in a right triangle other than the right angle, the sine is the ratio of the "leg" opposite that angle to the hypoteneuse length. The cosine is the ratio of the length of the "leg" adjacent to that angle to the hypoteneuse length. The tangent is the ratio of the length of the opposite "leg" to the adjacent "leg."
The normal sine and cosine functions have"ranges" between -1 and , inclusive. So they take on all real number values in this range......Thus, their values can be either "irrational"(non-repeating decimals like the "decimal" part of pi), or "rational" (can be expressed as a fraction) in this range, depending on the angle.
The tangent, (where defined), has a range from -∞ to +∞. It takes on all real number values - rational and irrational. Note, that for reasons I won't go into, the tangent isn't defined for certain angles!!
Hope that helps
