Can someone tell my what cos, sin and tan actually measure?
In: Mathematics
These functions measure ratios of sides of a right angled triangle. But to be more intuitive:
Stand a distance away from the room of your wall and raise your arm at any angle. Now you can probably guess if there was a line from your arm, it would probably hit that wall. The fun thing is, the height at which the line hits the wall has ratios with your distance from the wall and the distance from you to the point where the line touches the wall. Makes sense. Now the real fun part, for a given angle, say, hm, 45 degrees, whether it’s your arm or your friend’s arm, at any distance, the ratio will be the same. In fact, the ratio is same for any right angled triangle at 45 degrees.
Sin, cos, tan, are functions that give us the ratios. Say you know you’re 50 feet away from a 50 feet tall building. Then you know that the angle your feet make with the top of the building is 45 degrees, because the tan function tells us that at 45 degrees, the perpendicular (height of building) is equal to the base (distance from the building). So it’s real helpful in calculating stuff, cus everything likes to be in nice and tidy ratios for the same angles.
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