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Jace Burgess
Mathematics
17 June, 02:08
Why does sin (x) / cos (x) = tan (x) ?
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Dashawn Lee
17 June, 02:14
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Sin (x) = o/h
cos (x) = a/h
tan (x) = o/a
If we try to use o/h (sin) and a/h (cos) to write o/a (tan), it would look like:
o x h = o
h a a
o/h is sin
h/a is the inverse of cos (which is a/h)
when you divide by a fraction, you multiply by the inverse of the fraction. In this case, o/h (sin) is being divided by a/h (cos)
therefore sin (x) / cos (x) = tan (x)
another way of thinking about it is looking at a triangle.
To get the side opposite the angle x, you use sin (x)
to get the side adjacent to the angle x, you use cos (x)
because tan (x) = side opposite angle x / side adjacent angle x, then:
tan (x) = sin (x) / cos (x)
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