Q&A

the domain of both the sine and cosine functions is

The domain of the sine and cosine functions is all real numbers.

What is the domain of the cosine function is?

The domain of the function y=cos(x) is all real numbers (cosine is defined for any angle measure), the range is −1≤y≤1 .

Are the domain and range for the sine and cosine functions are the same?

Domain and range for sine and cosine functions There are no restrictions on the domain of sine and cosine functions; therefore, their domain is such that x ∈ R. Notice, however, that the range for both y = sin(x) and y = cos(x) is between -1 and 1.

Why is the domain of sin and cos all real numbers?

We can calculate the domain and range of cos(x). As we saw in the case of sin(x), for any point on a unit circle, the cos(x) is equal to adjacent / 1. The measure of adjacent can be defined for all the points on the circle, indicating that the angle x can take any value. So, the domain of cos(x) is all real numbers.

Are sine and cosine functions the same?

Sine and cosine — a.k.a., sin(θ) and cos(θ) — are functions revealing the shape of a right triangle. Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse , while cos(θ) is the ratio of the adjacent side to the hypotenuse .

What is the domain of cosine and sine?

The domain of the sine and cosine functions is all real numbers. The range of both the sine and cosine functions is [−1,1]. The sine and cosine of an angle have the same absolute value as the sine and cosine of its reference angle.

Does cosine have a domain?

Domain and range for sine and cosine functions There are no restrictions on the domain of sine and cosine functions; therefore, their domain is such that x ∈ R. Notice, however, that the range for both y = sin(x) and y = cos(x) is between -1 and 1.

What is the domain of the cosine function quizlet?

The Domain of the Cosine Function is what? It is the set of all real numbers.

Why is the domain of cosine all real numbers?

Function y=cos(x) is defined as the abscissa ( X -coordinate) of a point on a unit circle that corresponds to an angle of x radians. Therefore, the domain of this function is all real numbers from −∞ to +∞ .

Is the domain of sin function all real numbers?

Definition. Sine is an odd function and is periodic with period 2π . The sine function has a domain of all real numbers, and its range is −1≤sinx≤1 − 1 ≤ sin ⁡ x ≤ 1 .

Why is the domain of sin and cos what it is?

The domain of the sine and cosine functions is all real numbers. The range of both the sine and cosine functions is [−1,1]. The sine and cosine of an angle have the same absolute value as the sine and cosine of its reference angle.

Is the domain of the trigonometric functions sine and cosine all real numbers?

So yes, of the six trick functions only Sine and cosine has the domain of all real numbers, so true is the answer.

What are the only trigonometric functions with a domain of all real numbers?

Among those, there are only two functions namely sine function and cosine function whose domain is all real numbers (that is they are defined for all real values/ all values of…

Are sine and cosine functions the same?

Sine and cosine — a.k.a., sin(θ) and cos(θ) — are functions revealing the shape of a right triangle. Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse , while cos(θ) is the ratio of the adjacent side to the hypotenuse .

What is the domain and range of a cosine function?

The domain of the function y=cos(x) is all real numbers (cosine is defined for any angle measure), the range is −1≤y≤1 .

What is the domain and range of a sine function?

In the sine function, the domain is all real numbers and the range is -1 to 1.

What is are the domain and range of sine cosine and tangent functions?

Therefore, the domain of cosine function is x∈R. The range of sine function is -1 to 1. Therefore, we can say that the domain and range of cosine function is all a complex number. The tangent function has vertical asymptotes at ±(2n+1)π2.

What is the difference between sine function and cosine function?

Sine and cosine — a.k.a., sin(θ) and cos(θ) — are functions revealing the shape of a right triangle. Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse , while cos(θ) is the ratio of the adjacent side to the hypotenuse .

How are the sine and cosine functions similar?

The graphs of sine and cosine have the same shape: a repeating “hill and valley” pattern over an interval on the horizontal axis that has a length of . The sine and cosine functions have the same domain—the real numbers—and the same range—the interval of values .

Can cos and sin be the same?

You just verified the Complementary Angle Theorem: The sine of an angle is equal to the cosine of its complementary angle, and the cosine of an angle is equal to the sine of its complementary angle.

Are sin and cos graphs the same?

The graph of sine has the same shape as the graph of cosine. Indeed, the graph of sine can be obtained by translating the graph of cosine by ( 4 n + 1 ) π 2 \frac{(4n+1)\pi}{2} 2(4n+1)π​ units along the positive x x x-axis ( n n n is an integer).