 # Quick Answer: Can Cosine Be Negative?

## What is cosine to the negative 1?

With inverse cosine, we select the angle on the top half of the unit circle.

Thus cos-1 (–½) = 120° or cos-1 (–½) = 2π/3.

In other words, the range of cos-1 is restricted to [0, 180°] or [0, π].

Note: arccos refers to “arc cosine”, or the radian measure of the arc on a circle corresponding to a given value of cosine..

## Does sin or cos start at 0?

The Sine Function has this beautiful up-down curve (which repeats every 2π radians, or 360°). It starts at 0, heads up to 1 by π/2 radians (90°) and then heads down to −1.

## Why is it called cosine?

Similarly the cosine can be thought of as measuring the distance from the y-axis of that same point. It is useful to note that the cosine of an angle is the same as the sine of the complement of the angle. … The word sine originally came from the latin sinus, meaning “bay” or “inlet”.

## What is negative cosine equal to?

cos(-θ) = cos θ & sin(-θ) = – sin θ. These are the negative angle identities. Although the diagram shows the angle θ in the first quadrant, the same conclusion can be reached when θ lies in any quadrant, and so the negative angle identities hold for all angles θ.

## What is Y Sinx?

The graph of y=sin(x) is like a wave that forever oscillates between -1 and 1, in a shape that repeats itself every 2π units. … See how we find the graph of y=sin(x) using the ​unit-circle definition of sin(x).

## Can sin cos and tan be negative?

Note: Tangent is positive because dividing a negative by a negative gives a positive….Example: The sine, cosine and tangent of 210°Sinesin(210°) = −1 / 2 = −0.5Tangenttan(210°) = −1 / −1.732 = 0.5771 more row

## Where is sin cos and tan negative?

For an angle in the second quadrant the point P has negative x coordinate and positive y coordinate. Therefore: In Quadrant II, cos(θ) < 0, sin(θ) > 0 and tan(θ) < 0 (Sine positive). For an angle in the third quadrant the point P has negative x and y coordinates.

## What is the highest value of sin?

Maximum value of sin θ is 1 when θ = 90 ˚. Minimum value of sin θ is –1 when θ = 270 ˚. So, the range of values of sin θ is –1 ≤ sin θ ≤ 1.

## What does 2 pi n mean?

– GEdgar Dec 5 ’16 at 21:15. Think of the unit circle plotted on a Cartesian graph. x=cosθ, so cosθ≥0 for all values on and to the right of the y-axis. 2nπ comes from the fact that 2π is the period of the cosine function.

## How do you know if a cosine graph is negative?

Hare – sign is in front of the cosine graph. If we draw the negative cosine it will produce the reflection about the x – axis. So the negative cosine graph will be opposite to the positive graph.

## What’s the difference between a sin and cos graph?

In a cosine graph, a positive or negative number vertically flips the graph and determines whether the graph starts at the maximum (if it’s positive) or minimum (if it’s negative). For a sine graph, a positive or negative number vertically flips the graph like it does with a cosine graph.

## How do you convert sin into cos?

The Basic Two: Sine and Cosine(1) Memorize: sine = (opposite side) / hypotenuse. … (2) sin A = cos(90° − A) or cos(π/2 − A) cos A = sin(90° − A) or sin(π/2 − A)(3) Memorize: … (4) tangent = (opposite side) / (adjacent side)(5) Memorize: … (6) tan A = cot(90° − A) or cot(π/2 − A) … (7) sec A = csc(90° − A) or csc(π/2 − A)

## What is a cosine curve?

The Cosine Curve The x-coordinate of the point on the unit circle determined by a central angle (in standard position) of x radians is Cos(x). In a unit circle, the radian measure of an angle is the length of the arc subtended by that angle. … The angle x is shown in blue and the value of Cos(x) is shown in green.

## What is the inverse of cosine called?

Inverse Cosine: If you know the adjacent side of an angle and the hypotenuse in a right triangle, you can use inverse cosine to find the measure of the angle. Inverse cosine is also called arccosine and is labeled \begin{align*}\cos^{-1}\end{align*} or arccos.

## Is Arccos the same as inverse cos?

Arccos definition The arccosine of x is defined as the inverse cosine function of x when -1≤x≤1. (Here cos-1 x means the inverse cosine and does not mean cosine to the power of -1).

## Is SEC the inverse of cos?

The secant is the reciprocal of the cosine. The cotangent is the reciprocal of the tangent.

## Is Arccos the same as SEC?

Secant, cosecant and cotangent, almost always written as sec, cosec and cot are trigonometric functions like sin, cos and tan. Note, sec x is not the same as cos-1x (sometimes written as arccos x).