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If sin=3/5 what is cos,tan,csc, sec,cot?

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May 6, 2018

Answer:

#color(brown)(csc theta = 5/3#

#color(blue)(cos theta = 4/5, sec theta = 5/4#

#color(green)(tan theta = 3 / 4, cot theta = 4/3#

Explanation:

https://www.mathopenref.com/triangle345.html

#sin theta = "(Oppo. side) /( Hypotenuse)" = 3 / 5#

According to Pythagorus Theorem,

#"Adj. side " AB = sqrt ((AC)^2 - (BC)^2) = sqrt (5^2 - 3^2) = 4#

Any triangle whose sides are in the ratio 3:4:5 is a right triangle.

Such triangles that have their sides in the ratio of whole numbers are called #color(red)("Pythagorean Triples."#

There are an infinite number of them, and this is just the smallest.

#csc theta = 1/ sin theta = 5/3#

#cos theta = (AB) / (AC) = 4/5#

#sec theta = 1 / cos theta = 5/4#

#tan theta = (BC) / (AB) = 3 / 4#

#cot theta = 1 / tan theta = 4/3#

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