MHB Find the exact value of each of the remaining trigonometric functions of theta

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SUMMARY

The discussion focuses on finding the exact values of the remaining trigonometric functions given that \(\sin(\theta) = \frac{3}{5}\). Using the Pythagorean identity \(\sin^2(\theta) + \cos^2(\theta) = 1\), the cosine function can be calculated. Since \(\sin(\theta)\) is positive, \(\theta\) is located in either Quadrant I or II, which influences the signs of the other trigonometric functions derived from \(\theta\).

PREREQUISITES
  • Understanding of basic trigonometric functions
  • Familiarity with the Pythagorean identity
  • Knowledge of the unit circle and quadrants
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Calculate \(\cos(\theta)\) using the Pythagorean identity
  • Determine \(\tan(\theta)\) from \(\sin(\theta)\) and \(\cos(\theta)\)
  • Find \(\csc(\theta)\), \(\sec(\theta)\), and \(\cot(\theta)\) based on the values of \(\sin(\theta)\) and \(\cos(\theta)\)
  • Explore the implications of trigonometric functions in different quadrants
USEFUL FOR

Students studying trigonometry, educators teaching trigonometric identities, and anyone needing to solve problems involving trigonometric functions.

adrianaiha
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sin\theta 3/5
 
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I've moved this thread to our Trigonometry forum, since this is not a calculus problem, but involves trig. instead.

I am assuming you've been given:

$$\sin(\theta)=\frac{3}{5}$$

And you are to find the values of the other 5 trig. functions as a function of $\theta$.

Since the sine of $\theta$ is positive, we know that $\theta$ is in either Quadrant I or II. To find the cosine of $\theta$, let's consider the Pythagorean identity:

$$\sin^2(\theta)+\cos^2(\theta)=1$$

Solve this for $\cos(\theta)$, and plug in the given value for $\sin(\theta)$...what do you get?
 

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