0
Think of tangent as sin divided by cos or sin/cos. Now cos 90 degrees is 0 so tan90 would be 1/0 which is not define since you are now allowed to divide by 0. It's best to visualize what Tan(90) means: Take a typical right angle triangle: From the angle in question (A), you have the adjacent leg (The leg extending from angle A to the right angle opposite), the opposite leg (the leg directly opposite the angle A, of course) and the hypotenuse (the leg intersecting the aforementioned two legs) Tan(A) is the ratio of the opposite leg and the adjacent leg. To solve for Tan (A): Tan (A) = opposite/adjacent. As angle (A) increases, the length of the opposite side also increases. So what happens at A=90? Well, you no longer have a triangle! The hypotenuse (the leg that intersects the opposite side from the adjacent side) NEVER INTERSECTS. Therefore, no longer being a triangle, you can no longer define the ratio.
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