MHB Find All Trig Functions of Gamma Given cot(gamma)=4/3

AI Thread Summary
Given cot(gamma) = 4/3, the triangle formed has sides AC = 4, BC = 3, and AB = 5, which is derived using the Pythagorean theorem. From this, the sine, cosine, and tangent functions can be calculated: sin(gamma) = 3/5, cos(gamma) = 4/5, and tan(gamma) = 3/4. Additionally, the cosecant, secant, and cotangent functions are found to be csc(gamma) = 5/3, sec(gamma) = 5/4, and cot(gamma) = 4/3, confirming the initial condition. All five remaining trigonometric functions of gamma have been successfully determined. This solution illustrates the relationship between the cotangent and the other trigonometric functions.
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Given cot(gamma)=4/3 find all possible values of the five remaining trigonometric functions of γ.

Could somebody help me here?
Thanks
 
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Let's make a diagram.

\begin{tikzpicture}
\draw (0,0) node[anchor=north]{$A$}
-- (4,0) node[anchor=north]{$C$}
-- (4,4) node[anchor=south]{$B$}
-- cycle;
\end{tikzpicture}

Using the given information and Pythagoras:

$$\overline{AC}=4\quad\overline{BC}=3\quad\overline{AB}=5$$

Now, can you determine the five remaining trigonometric ratios?
 
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