Читать книгу U Can: Physics I For Dummies - Steven Holzner - Страница 15

You need to know a little trigonometry, including the sine, cosine, and tangent functions, for physics problems. To find these values, start with a simple right triangle. Take a look at Figure 2-1, which displays a right triangle in all its glory, complete with labels I’ve provided for the sake of explanation. Note in particular the angle , which appears between one of the triangle’s legs and the hypotenuse (the longest side, which is opposite the right angle). The side y is opposite , and the side x is adjacent to .

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Figure 2-1: A labeled triangle that you can use to find trig values.

Remember: To find the trigonometric values of the triangle in Figure 2-1, you divide one side by another. Here are the definitions of sine, cosine, and tangent:

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If you’re given the measure of one angle and one side of the triangle, you can find all the other sides. Here are some other forms of the trig relationships – they’ll probably become distressingly familiar before you finish any physics course, but you don’t need to memorize them. If you know the preceding sine, cosine, and tangent equations, you can derive the following ones as needed:

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To find the angle , you can go backward with the inverse sine, cosine, and tangent, which are written as sin^– 1, cos^– 1, and tan^– 1. Basically, if you input the sine of an angle into the sin^– 1 equation, you end up with the measure of the angle itself. Here are the inverses for the triangle in Figure 2-1:

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And here’s one more equation, the Pythagorean theorem. It gives you the length of the hypotenuse when you plug in the other two sides:

If you need a more in-depth refresher, check out Trigonometry For Dummies, by Mary Jane Sterling (Wiley).

Example

Q. If the side labeled x in Figure 2-1 is 30 centimeters, and the angle θ is 30 degrees, what is the length of the hypotenuse, rounded to the nearest centimeter?

A. The correct answer is 35 centimeters.

1. Solve the equation for h to get

2. Plug in the given values:

Practice Questions

1. Given the hypotenuse h and the angle θ, what is the length x equal to?

2. If x = 3 m and y = 4 m, what is the length of the hypotenuse?

Practice Answers

1. x = hcosθ. Your answer comes from the definition of cosine.

2. 5 m. Start with the Pythagorean theorem:

Plug in the numbers, and work out the answer: