Limits of trigonometric functions worksheet

1. What are the 12 trig functions?
2. What are all 6 trigonometric functions?
3. Do sin and cos functions have limits?
4. What are the 4 concepts of trigonometry?
5. What are the 3 basic trigonometry functions?
6. What are 5 key points of a trig function?
7. What is the limit LIMX → ∞ XSIN 1x?
8. What is the limit of sin theta?
9. How do you determine the limit of a function?
10. How do you restrict the sine function?
11. How do you find the limit of a COSX?
12. Why are trig functions restricted?
13. What are the rules of limit of functions?
14. What is the restricted domain of cos?
15. What is the domain of sin?
16. What are the restrictions of tangent?
17. What is the maximum of Sinx COSX?
18. What is the max value of COSX?

What are the 12 trig functions?

The historical answer: At least 12

These are versine, haversine, coversine, hacoversine, exsecant, and excosecant. All of these can be expressed simply in terms of more familiar trig functions. For example, versine(θ) = 2 sin²(θ/2) = 1 – cos(θ) and exsecant(θ) = sec(θ) – 1.

What are all 6 trigonometric functions?

These six functions and their abbreviations are sine (sin), cosine (cos), tangent (tan), secant (sec), cosecant (csc), and cotangent (cot). The values of these functions for any real number x are denoted by sin x, cos x, etc.

Do sin and cos functions have limits?

The trigonometric functions sine and cosine have four important limit properties: You can use these properties to evaluate many limit problems involving the six basic trigonometric functions. Example 1: Evaluate .

What are the 4 concepts of trigonometry?

The three basic functions in trigonometry are sine, cosine and tangent. Based on these three functions the other three functions that are cotangent, secant and cosecant are derived.

What are the 3 basic trigonometry functions?

The angles of sine, cosine, and tangent are the primary classification of functions of trigonometry.

What are 5 key points of a trig function?

They are the three x-intercepts, the maximum point, and the minimum point. All of these are on your unit circle. The values of sin x correspond to the y-values, so those key points are (angle, y-value) or (0,0), (π/2, 1), (π, 0), (3π/2, -1), (2π, 0).

What is the limit LIMX → ∞ XSIN 1x?

3 Answers. limx→∞xsin(1x)=1 . Let us look at some details. Instead of l'Hopital's Rule, one can use the fundamental trigonometric limit: limh→0sinhh=1 .

What is the limit of sin theta?

to give you a quick outline of the key elements of the proof that if θ is in radians, then this limit is equal to 1.

How do you determine the limit of a function?

A function is said to have a limit if it has a two-sided limit. A graph provides a visual method of determining the limit of a function. If the function has a limit as x approaches a, the branches of the graph will approach the same y− coordinate near x=a from the left and the right.

How do you restrict the sine function?

SINE: We restrict the domain to [−π/2,π/2] to ensure our function is one-to-one. By definition, sin−1(x) is the angle in [−π/2,π/2] whose sine is x. This only makes sense if −1≤x≤1. θ=sin−1(x)⟺sin(θ)=x, for −π/2≤θ≤π/2.

How do you find the limit of a COSX?

The limit does not exist. Most instructors will accept the acronym DNE. The simple reason is that cosine is an oscillating function so it does not converge to a single value. A related question that does have a limit is limx→∞cos(1x)=1 .

Why are trig functions restricted?

The restricted-domain cosine function and its inverse are graphed below. The domains of the other four basic trig. functions are restricted appropriately so that they and their inverses can be defined and graphed. denoted by " " is defined to be the inverse of the domain-restricted tangent function.

What are the rules of limit of functions?

Product law for limits states that the limit of a product of functions equals the product of the limit of each function. Quotient law for limits states that the limit of a quotient of functions equals the quotient of the limit of each function.

What is the restricted domain of cos?

The restriction that is placed on the domain values of the cosine function is 0 ≤ x ≤ π (see Figure 2 ). This restricted function is called Cosine.

What is the domain of sin?

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

What are the restrictions of tangent?

Since tangent is not a one-to-one function, the domain must be limited to -pi/2 to pi/2, which is called the restricted tangent function. The graph of the inverse tangent function is a reflection of the restricted tangent function over y = x.

What is the maximum of Sinx COSX?

Therefore, maximum value of 2 .

What is the max value of COSX?

The maximum value of cosx is 1. At x = 0° and x = 360°, cosx = 1. The minimum value of cosx is −1. At x = 180°, cosx = −1.