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Chapter 10: Problem 50

Describe one similarity and one difference between the sine ratio and the cosine ratio in terms of the sides of a right triangle.

Short Answer

Expert verified
The similarity between the sine and cosine ratios is that they both involve a ratio of two sides of a right triangle, one of which is the hypotenuse. The difference between them is that sine uses the side opposite the angle, while cosine uses the side adjacent to the angle.

Step by step solution

01

Defining Sine Ratio

The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. So, we can write this as \(sin(胃) = \frac{OppositeSide}{Hypotenuse}\).
02

Defining Cosine Ratio

The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. We can write \(cos(胃) = \frac{AdjacentSide}{Hypotenuse}\).
03

Identifying Similarity

The similarity between the sine and cosine ratios is that they both involve a ratio of two sides of a right triangle to each other, and in both cases, one of those sides is the hypotenuse.
04

Identifying Difference

The difference between the two, however, lies in the side of the triangle that is not the hypotenuse. For sine, it is the side opposite the angle, and for cosine, it is the side adjacent to the angle.

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Most popular questions from this chapter

In the diagram for Exercises \(17-19\), suppose that you are not told that \(\triangle A B C\) and \(\triangle A D E\) are similar. Instead, you are given that \(\overleftrightarrow{E D}\) and \(\overleftrightarrow{C B}\) are parallel. Under these conditions, explain why the triangles must be similar.

Use the Pythagorean Theorem to solve Exercises 39-46. Use your calculator to find square roots, rounding, if necessary, to the nearest tenth. A flagpole has a height of 10 yards. It will be supported by three cables, each of which is attached to the flagpole at a point 4 yards below the top of the pole and attached to the ground at a point that is 8 yards from the base of the pole. Find the total number of yards of cable that will be required.

Explain why the sine or cosine of an acute angle cannot be greater than or equal to 1 .

The hour hand of a clock moves from 1 to 7 o'clock. Through how many degrees does it move?

What does it mean if a graph is traversable?
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