Find Largest Angle: Sine & Tangent to Within 2 SF

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In summary, for small angles theta, the numerical value of sin theta is approximately the same as the numerical value of tan theta. To find the largest angle for which sine and tangent agree to within two significant figures, one can use the Taylor series approximations of sin and tan, taking the difference to capture the fact that they are different series. It is important to show effort and use the appropriate forums when seeking help.
  • #1
homeworkboy
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For small angles theta, the numerical value of sin theta is approximately the same as the

numerical value of tan theta.Find the largest angle for which sine and tangent agree to within

two significant figures.

thank you!
 
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  • #2
anyone? please i would greatly appreciate it if someone helped me on this. Thank You
 
  • #3
You could just grab your calculator and figure it out.
 
  • #4
Some hints about getting help.
1. Post in the correct forum, we have homework help forums. Use them.
2. Show that you have at least tried something.


For your problem. Look at the Taylor series approximations of sin and Tan. Use enough of the series for each to capture the fact that they are different seriss. Take the difference.
 

1. What is the meaning of "Find Largest Angle: Sine & Tangent to Within 2 SF"?

The phrase "Find Largest Angle: Sine & Tangent to Within 2 SF" refers to a mathematical problem where one must find the largest angle that can be calculated using the sine and tangent functions within a certain level of accuracy, specifically within 2 significant figures.

2. What are the sine and tangent functions used for?

The sine and tangent functions are mathematical tools used to calculate the relationship between the sides and angles of a right triangle. They are commonly used in trigonometry and geometry.

3. How do you find the largest angle using the sine and tangent functions?

To find the largest angle using the sine and tangent functions, you would first need to know at least two sides of a right triangle. Then, you can use the sine and tangent ratios to calculate the angles. The largest angle would be the one with the highest value obtained from the calculations.

4. What is the significance of 2 significant figures in this problem?

The 2 significant figures in this problem indicate the level of accuracy required in the final answer. This means that the final angle calculated must be rounded to 2 decimal places.

5. Are there any other methods to find the largest angle in a right triangle?

Yes, there are other methods such as using the cosine function or the Pythagorean theorem. However, using the sine and tangent functions is a common and efficient way to find the largest angle in a right triangle.

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