Can someone tell my what cos, sin and tan actually measure?
In: Mathematics
To a five year old: think of a fly sitting on the edge of a table fans blade. Sin and cos are machines that can tell you how far away the fly is from the middle of the fan. The machines don’t work unless you tell them the angle the fans blade makes from the surface of the table. Cos will tell you the horizontal (left or right) distance from the middle while sin tells you the vertical (up or down) distance from the middle.
Here let’s pull out a calculator because it has the sin and cos machines on it. See this table fan? Its blade is 1 ft. long. Right now the fly is sitting on the edge and the fan blade is sticking straight out to the right. So the angle this blade is making is 0 degrees. How far to the right is the fly from the middle? That’s right it’s 1ft away, here let’s use the cos machine to double check cos(0) = 1 !
Now how far above is the fly from the middle? That’s right it’s 0ft above the middle of the fan because they’re at the same height right now. Let’s check with the machine: sin(0) = 0 !
Left rotate the fan so the fly is now straight up from the middle. The fan blade is now making a 90 degree angle from the desk. How far away (left/right) is the fly to the middle how? That’s right it’s 0ft! Let’s check: cos(90) = 0. And now how far above is the fly from the middle? That’s right it’s now 1 ft. above the fly! Let’s check: sin(90) = 1
In a nut shell:
cos(angle) = horizontal distance from origin
sin(angle) =. Vertical distance from origin
cos and sin are the main functions here but we like tangent as well as it’s the ratio of sin/cos
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