If sin s =2/3 and cos s = √5 over 3 what are the values of the remaining four trigonometric functions of s?

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Answer 1 · 2018-02-21T04:52:57

As below

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Given #sin s = a / c = 2/3#

#:. a = 2, c = 3#

Similarly, #cos s = b / a = sqrt5 / 3#

#:. b = sqrt5, c = 3#

Verification :

As per Pythagoras theorem,

#c^2 = a^2 + b^2#

L H S = #c^2 = 3^2 = 9#

R H S = #a^2 + b^2 = 2^2 + (sqrt5)^2 = 4 + 5 = 9#

Hence proved.

Other trigonometric functions :

#tan s = a / b = 2 / sqrt5#

#csc s = 1 / sin s = 1 / (2/3) = 3/2#

#sec s = 1 / cos s = 1 /(sqrt5/3) = 3 / sqrt5#

#cot s = 1 / tan s = 1 / (2 / sqrt5) = sqrt5 / 2#