MHB Find Exact Values of Cosθ, Cscθ & Tanθ | Point (-3,2)

Thread starter sphrrson
Start date May 10, 2015
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To find the exact values of cosθ, cscθ, and tanθ for the point (-3, 2), one must first determine the lengths of the sides of the right triangle formed by this point in relation to the origin. The hypotenuse can be calculated using the Pythagorean theorem, yielding a length of √13. From this, cosθ is found as adjacent/hypotenuse, giving -3/√13, while cscθ is the reciprocal of sinθ, calculated as hypotenuse/opposite, resulting in √13/2. Finally, tanθ is derived as opposite/adjacent, resulting in -2/3. This method effectively provides the exact trigonometric values based on the coordinates of the point.

May 10, 2015

sphrrson

Let (-3, 2) be a point on the terminal side of θ. Find exact values of cosθ, cscθ, and tanθ?

Can anyone help!?

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May 10, 2015

Jameson

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MHB

Hi sphrrson,

Welcome to MHB! :)

Can you show us what you've tried? How do we find the value of something like $\sin(\theta)$ if we know the legs of the triangle? What would this triangle look like?

Thread 'More similar triangle problems'

For the sake of argument, lets assume this is, in fact, a right triangle with a rectangle inscribed in it. Here is what looks like a very elegant solution: Triangles A and B are similar a/4=2/b ab=8 But what is happening in that second line? Is there a property of similar triangles I'm forgetting?

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