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

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SUMMARY

The discussion focuses on finding all trigonometric functions of angle γ given that cot(γ) = 4/3. Using the Pythagorean theorem, the sides of the right triangle are determined as AC = 4, BC = 3, and AB = 5. Consequently, the five remaining trigonometric functions can be calculated as follows: sin(γ) = 3/5, cos(γ) = 4/5, tan(γ) = 3/4, sec(γ) = 5/4, and csc(γ) = 5/3.

PREREQUISITES
  • Understanding of trigonometric functions and their definitions
  • Knowledge of the Pythagorean theorem
  • Familiarity with right triangle properties
  • Basic skills in diagramming geometric figures
NEXT STEPS
  • Study the unit circle and its relation to trigonometric functions
  • Learn how to derive trigonometric identities
  • Explore the applications of trigonometric functions in real-world problems
  • Practice solving problems involving right triangles and trigonometric ratios
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Students studying trigonometry, educators teaching trigonometric concepts, and anyone interested in solving geometric problems involving angles and triangles.

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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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