How would you describe the graphs of the sine and cosine functions?
How would you describe the graphs of the sine and cosine functions?
The sine and cosine functions have several distinct characteristics: They are periodic functions with a period of 2π. The graph of y = sin x is symmetric about the origin, because it is an odd function. The graph of y = cos x is symmetric about the y-axis, because it is an even function.
How can you tell the difference between a sine and cosine graph?
The graph of the cosine is the darker curve; note how it’s shifted to the left of the sine curve. For example, cosθ = sin (90° – θ) means that if θ is equal to 25 degrees, then cos 25° = sin (90° – 25°) = sin 65°.
What are the properties of sine and cosine functions?
The sine and cosine functions have several distinct characteristics:
- They are periodic functions with a period of.
- The domain of each function is ( − ∞ , ∞ ) and the range is.
- The graph of y = sin x y = sin x is symmetric about the origin, because it is an odd function.
How does the sine function work?
In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse. In any right triangle, the sine of an angle x is the length of the opposite side (O) divided by the length of the hypotenuse (H).
What is the use of COS function?
The cosine function is a periodic function which is very important in trigonometry. The simplest way to understand the cosine function is to use the unit circle. For a given angle measure θ , draw a unit circle on the coordinate plane and draw the angle centered at the origin, with one side as the positive x -axis.
What features are unique to sine and cosine graphs?
The sine and cosine functions have several distinct characteristics:
- They are periodic functions with a period of.
- The domain of each function is and the range is.
- The graph of is symmetric about the origin, because it is an odd function.
- The graph of is symmetric about the axis, because it is an even function.
Why are the sine and cosine functions called periodic functions?
1) Why are the sine and cosine functions called periodic functions? This means that the function values repeat for every P units on the x-axis.
Why are sine and cosine functions called periodic functions?
What does cosine find?
more In a right angled triangle, the cosine of an angle is: The length of the adjacent side divided by the length of the hypotenuse. The abbreviation is cos.
Where is cosine defined?
English Language Learners Definition of cosine : the ratio between the long side (called the hypotenuse) and the side that is next to an acute angle in a right triangle.
What does sine, cosine, and tangent actually do?
In this career, sine, cosine, and tangent are sometimes used to determine the size of large sea creatures from a distance, and also to calculate light levels at certain depths to see how they affect photosynthesis. There are dozens of careers that use trigonometry in their daily tasks.
What are the six trigonometry functions?
The six main trigonometric functions are sine, cosine, tangent, secant, cosecant, and cotangent. They are useful for finding heights and distances, and have practical applications in many fields including architecture, surveying, and engineering.
How could you describe the sine function?
They are periodic functions with a period of 2π.
What are the properties of sine function?
Sine: Properties. The sine function has a number of properties that result from it being periodic and odd. Most of these should not be memorized by the reader; yet, the reader should be able to instantly derive them from an understanding of the function’s characteristics. The sine function is periodic with a period of 2p, which implies that.