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.
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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?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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