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

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Thread starter sphrrson
Start date May 10, 2015
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In summary, to find the exact value of a trigonometric function (cosθ, cscθ, or tanθ) at a specific point, first determine the angle (θ) using the coordinates given, and then use a unit circle or trigonometric identities to solve for the function. This is important because it allows for accurate problem-solving and has practical applications in various fields. Calculators can also be used, but understanding the concepts is crucial for accuracy.

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

Gold Member

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?

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

How do I find the exact value of cosθ at a specific point?

To find the exact value of cosθ at a specific point, first determine the angle (θ) using the coordinates given. Then, use a unit circle or trigonometric identities to solve for cosθ. In this case, since the point is (-3,2), the angle θ is in the second quadrant, and the formula for cosθ is cosθ = adjacent/hypotenuse. Therefore, cosθ = -3/√(3^2 + 2^2) = -3/√13.

How do I find the exact value of cscθ at a specific point?

To find the exact value of cscθ at a specific point, first determine the angle (θ) using the coordinates given. Then, use a unit circle or trigonometric identities to solve for cscθ. In this case, since the point is (-3,2), the angle θ is in the second quadrant, and the formula for cscθ is cscθ = hypotenuse/opposite. Therefore, cscθ = √(3^2 + 2^2)/2 = √13/2.

How do I find the exact value of tanθ at a specific point?

To find the exact value of tanθ at a specific point, first determine the angle (θ) using the coordinates given. Then, use a unit circle or trigonometric identities to solve for tanθ. In this case, since the point is (-3,2), the angle θ is in the second quadrant, and the formula for tanθ is tanθ = opposite/adjacent. Therefore, tanθ = 2/-3 = -2/3.

Can I use a calculator to find the exact values of cosθ, cscθ, and tanθ?

Yes, you can use a scientific or graphing calculator to find the exact values of cosθ, cscθ, and tanθ. However, it is important to know the formulas and understand the concepts behind these trigonometric functions to ensure accuracy and avoid errors.

Why is it important to find the exact values of trigonometric functions at a specific point?

Finding the exact values of trigonometric functions at a specific point is important because it allows us to accurately solve various mathematical problems and equations involving triangles and angles. These values also have real-life applications in fields such as engineering, physics, and navigation.