Solving a Trigonometry Problem: Need Help!

In summary, in order to determine which trigonometric ratio to use, you must first identify the given information. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem is used in trigonometry to find missing sides. To find a missing angle, you can use inverse trigonometric functions. Trigonometry is used in real-life applications. Some common mistakes to avoid when solving a trigonometry problem are using the wrong ratio, forgetting to convert units, and not using the Pythagorean theorem when needed.
  • #1
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gif.latex?\int%20\frac{1}{x^2\sqrt{x^2+4}}dx.gif


So I'm not really sure how to go about this problem. I've attempted letting x = a few things. 4sinx, and 4tanx. Maybe trig substitution is not even the way to go. Could someone push me in the right direction?
 
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  • #2
Yes x=2tanθ should work. Try it out and post back if you do not get through.
 

1. How do I know which trigonometric ratio to use?

In order to determine which trigonometric ratio to use, you must first identify the given information. If you are given two sides of a right triangle, you can use the sine, cosine, or tangent ratio. If you are given one side and one angle of a right triangle, you can use the cosine or tangent ratio. If you are given two angles of a right triangle, you can use the sine or cosine ratio.

2. What is the Pythagorean theorem and how is it used in trigonometry?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem is used in trigonometry to find the length of a missing side in a right triangle using the sine, cosine, or tangent ratios.

3. How do I find the missing angle in a right triangle?

To find a missing angle in a right triangle, you can use the inverse trigonometric functions (arcsine, arccosine, arctangent) to solve for the angle. First, determine which trigonometric ratio to use based on the given information. Then, use the inverse function to solve for the angle.

4. Can trigonometry be used in real-life problems?

Yes, trigonometry is used in many real-life applications such as architecture, engineering, navigation, and physics. It is used to calculate distances, heights, angles, and forces in various situations.

5. What are some common mistakes to avoid when solving a trigonometry problem?

Some common mistakes to avoid when solving a trigonometry problem include using the wrong trigonometric ratio, forgetting to convert units, and not using the Pythagorean theorem when needed. It is also important to carefully label the given information and the unknown variable in the diagram to avoid confusion.

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