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Questions and Answers
What does the sine function relate in a right triangle?
What does the sine function relate in a right triangle?
- Length of the side opposite to the right angle to the hypotenuse
- Length of the side opposite to an acute angle to the hypotenuse (correct)
- Length of the hypotenuse to the side adjacent to an acute angle
- Length of both sides adjacent to the right angle
What does the cosine function relate in a right triangle?
What does the cosine function relate in a right triangle?
- Length of the adjacent side to the hypotenuse (correct)
- Length of the side adjacent to an acute angle to the hypotenuse
- Length of the hypotenuse to the opposite side
- Length of both sides opposite to the right angle
In terms of angles in a right triangle, what does the tangent function relate?
In terms of angles in a right triangle, what does the tangent function relate?
- Ratio of hypotenuse to opposite side
- Ratio of adjacent side to opposite side
- Ratio of opposite side to hypotenuse (correct)
- Ratio of adjacent side to hypotenuse
Which trigonometric function can be expressed as the ratio of sine over cosine?
Which trigonometric function can be expressed as the ratio of sine over cosine?
What are the three primary trigonometric functions that form the basis of many calculations involving angles?
What are the three primary trigonometric functions that form the basis of many calculations involving angles?
Which function assigns to each non-negative real number x the ratio of length of adjacent side to hypotenuse?
Which function assigns to each non-negative real number x the ratio of length of adjacent side to hypotenuse?
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Study Notes
Trigonometric Functions
Trigonometry is a branch of mathematics that deals with triangles and their relationships with angles and sides. It uses functions that relate an angle of a triangle to ratios of its side lengths. Here's a brief overview of these trigonometric functions:
Sine Function
The sine function assigns to each non-negative real number x the ratio of the length of the side opposite to an acute angle θ in a right triangle to the length of the hypotenuse; in other words, it is the tangent of π/2 minus the angle θ.
Cosine Function
The cosine function assigns to each non-negative real number x the ratio of the length of the adjacent side to the length of the hypotenuse of a right triangle whose vertex is at (x, 0).
Tangent Function
The tangent function assigns to each non-zero real number x the ratio of the length of the side opposite to an angle θ in a right triangle to the length of the adjacent side. It can also be expressed as the ratio of the difference between the sine and cosine, or the sine over the cosine.
These three trigonometric functions form the basis of many calculations involving angles of various sizes and shapes, particularly those related to circles. They are used extensively in fields such as physics, engineering, computer science, and more.
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