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

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Given that sin(θ) = 3/5, the discussion focuses on finding the remaining trigonometric functions. Since sin(θ) is positive, θ is in Quadrant I or II. Using the Pythagorean identity sin²(θ) + cos²(θ) = 1, cos(θ) can be calculated as √(1 - (3/5)²), resulting in cos(θ) = 4/5. The values for tan(θ), sec(θ), csc(θ), and cot(θ) can then be derived from sin(θ) and cos(θ). The thread emphasizes the importance of understanding trigonometric identities for solving such problems.
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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