If sin s =2/3 and cos s = โˆš5 over 3 what are the values of the remaining four trigonometric functions of s?

1 Answer
Feb 21, 2018

As below

Explanation:

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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