Determine the approximate values of sinθ and cosθ from the diagram below

In summary, the conversation is about determining the approximate values of sinθ and cosθ from a diagram. The formula for finding these values is mentioned and it is stated that the values depend on the angle θ, which is not marked on the diagram. A possible angle that θ could represent is also mentioned.
  • #1
SarahJeen
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View attachment 863
The answer I got was: View attachment 864
If I'am wrong please explain the correct solution and explain your reasoning thanks sarah (Sun)
 

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  • #2
Re: Determine the approximate values of sinθ and cosθ from the digram below

If your points are on the unit circle centred at the origin, then \(\displaystyle \displaystyle \begin{align*} x = \cos{(\theta)} \end{align*}\) and \(\displaystyle \displaystyle \begin{align*} y = \sin{(\theta)} \end{align*}\).
 
  • #3
SarahJeen said:
Determine the approximate values of sinθ and cosθ from the diagram below
This, of course, depends on what $\theta$ is since it is not marked on the diagram. Maybe it's the angle made by the axis of symmetry of the letter "o" in the Google logo (which is typeset in the Catull font). (Smile)

OCiJKUb.png
 

FAQ: Determine the approximate values of sinθ and cosθ from the diagram below

How do I determine the approximate values of sinθ and cosθ from the diagram?

To determine the approximate values of sinθ and cosθ from the diagram, you can use the right triangle formed by the given angle. Simply divide the opposite side of the triangle by the hypotenuse to find the value of sinθ, and divide the adjacent side by the hypotenuse to find the value of cosθ.

Do I need to use a calculator to find the approximate values of sinθ and cosθ?

No, you do not need a calculator to find the approximate values of sinθ and cosθ. As long as you have the given angle and can use basic trigonometric principles, you can determine the approximate values without a calculator.

Can I use this method for any angle, or only for acute angles?

This method can be used for any angle, including acute, right, and obtuse angles. However, for obtuse angles, you may need to use the negative value of sinθ or cosθ, depending on which quadrant the angle is located in.

How accurate are the approximate values of sinθ and cosθ from this method?

The accuracy of the approximate values depends on the precision of the given information and the accuracy of your calculations. Generally, the more precise the information and the more accurate your calculations, the closer the approximate values will be to the exact values.

Can I use this method to find the exact values of sinθ and cosθ?

No, this method will only give you approximate values of sinθ and cosθ. To find the exact values, you will need to use a calculator or refer to a trigonometric table. However, the approximate values can still be very useful in many applications.

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