cosec theta = a so i know sine = 1/a
i am asked to find the other 4 ratios.

cos = sqrt 1-(1/a)^2

The answer given is sqrt (a^2-1)/a

this is wrote different as i do not know how to enter the symbols etc.

i do not see how this is the answer my answer was sqrt 1-1/a^2
and the hypotenuse terminates in quadrant 1.
Guest Feb 1, 2012

\(\text{Your answer is:}\sqrt{1-(\frac{1}a)^2}\\ \text{But the answer is:}\frac{\sqrt{a^2-1}}{a}\)

\(\sin\theta = \frac{1}{a}\\\text{Opposite side of }\theta = 1\\\text{Hypotenuse}=a \\\therefore \text{Adjacent side of }\theta = \sqrt{a^2-1}\text{<---- Pythagoras' Theorem}\\ \therefore\cos\theta = \dfrac{\text{Adjacent side}}{\text{Hypotenuse}}\\\qquad\quad=\dfrac{\sqrt{a^2-1}}{a}\)

MaxWong  Jul 17, 2016

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