## How big can sin be?

SIn and Cos values can’t be greater than 1 because limits of Sin and Cos functions are from -1 to 1 so they can’t exceed 1.

## What is the range of sin x?

out inverse sines. The function f(x) = sin x has all real numbers in its domain, but its range is −1 ≤ sin x ≤ 1. The values of the sine function are different, depending on whether the angle is in degrees or radians. The function is periodic with periodicity 360 degrees or 2π radians.

**Can a sine value be greater than 1?**

A = 1 is if a = c, but that would make for a strange triangle!), the sine ratio cannot be greater than 1. Figure 20.4 A right triangle with side lengths a and b, and hypotenuse length c.

**Is Sinx always less than X?**

The derivative of sin x is cos x. That derivative starts with 1 and steadily becomes less. So the sin x does not increase as much as x so it becomes less with increasing x.

### Is sin an XR or a yr?

THE UNIT CIRCLE

sin θ | = | y r |
---|---|---|

cos θ | = | x r |

tan θ | = | y x |

### What is the maximum of f/x sin x?

1

The maximum of f(x) = sin(x) is 1.

**How do you graph sin x?**

Graph of Sinx

- Draw a Y-axis with 0,1,-1 …on it.
- From the origin draw an X-axis. a) if you want a graph in π then mark the points π/2, π,3π/2, 2π etc.
- y = a sin(x) the amplitude ‘a’ is 1 so the curve will be up to (0,1). If y = 2 sin(x) then the amplitude will be 2, so the curve will be up to (0,2).

**Why is sin always less than 1?**

The simple reason is that the length of the sides of a right triangle are always less than the length of the hypotenuse. So, the ratio of any side and hypotenuse is always less than 1.

#### Why is the sine of an acute angle less than one?

Sine and Cosine are the trignomatric ratios, whose values are less that 1 for an acute angle. An acute angle is angle greater than 0 degree but less than 90 degrees. Since both Sine and Cosine has the value 1 at angles 90 degrees and 0 degree respectively.

#### What is the derivative of sin x with increasing x?

The derivative of x is 1 so the line steadily increases. The derivative of sin x is cos x. That derivative starts with 1 and steadily becomes less. So the sin x does not increase as much as x so it becomes less with increasing x.

**What is the range of cos θ and sin θ?**

Notice that Thus, cos θ = x/ r and sin θ = y/r cannot be greater than 1 or less than −1, depending on whether x and y are positive or negative (r = x when y = 0 and r = y when x = 0). So we conclude that the range of cos θ and sin θ is, {y | − 1 ≤ y ≤ 1} .

**How do you show it’s less than X for positive x?**

To show it’s less than x for positive x, look at a circle. A circular arc is longer than the chord connecting its end points (because it’s not a straight line) which itself is longer than either leg of the right triangle of which it is the hypotenuse, of which one is equal to the sine of that arc. 8 clever moves when you have $1,000 in the bank.

## What is the period of SiNx and cscx?

The period of cscx is the same as that of sinx, which is 2…. Since sinx is an odd function, cscx is also an odd function. Finally, at all of the points where cscx is undeﬁned, the function has both left and right vertical asymptotes, but just as in the case of secx, the behavior of the vertical asymptotes depends on the point.