## Why is r cos theta a circle?

r = a cos θ is a circle where “a” is the diameter of the circle that has its left-most edge at the pole. The limaçons containing sine will be above the horizontal axis if the sign between a and b is plus or below the horizontal axis if the sign if minus.

## Why is Cos minus theta is equal to cos theta?

Since the cosine is the x -coordinate of the points on the unit circle, you see that the two points have the same cosine, and opposite sine. In fact, the cosine is an even function, which means exactly that cos(x)=cos(−x) , while the sine is odd, which means that sin(x)=−sin(−x) .

**Why is sin the Y value?**

So z = sin(θ) which means that the length of the line between the x-axis and the point on the circle is sin(θ). This is why the y-axis is called the “sine” – that’s what it represents on a triangle.

### Is sin theta always less than 1?

the value of sin and Cos is always less than 1 because sin is equals two perpendicular ÷ hypotenuse and perpendicular is always smaller than hypotenuse so it is not possible that sin is greater than 1 same case in cos also cos is equals to base divided by hypotenuse and base is always smaller than hypotenuse so it is …

### What does r cos theta mean?

As an alternative we define a new coordinate system where the first coordinate r is the distance from the origin to the point and the second coordinate theta is the angle that the ray from the origin to the point makes with the positive x axis. From trigonometry, we have. x = rcos theta.

**Why is sin theta equal to?**

In the context of a right angle, the sine function, written as sinθ is equal to the division of the opposite side of the reference angle (θ) by the hypotenuse, or long side, of the triangle.

## Why does sin 90 theta )= cos theta?

Patterns of right triangles. All triangles have 3 angles that add to 180 degrees. Therefore, if one angle is 90 degrees we can figure out Sin Theta = Cos (90 – Theta) and Cos Theta = Sin (90 – Theta).

## How to find the value of arcsin(0) from sin(Theta)?

Precalculus. Solve for? sin (theta)=0. sin(θ) = 0 sin ( θ) = 0. Take the inverse sine of both sides of the equation to extract θ θ from inside the sine. θ = arcsin(0) θ = arcsin ( 0) The exact value of arcsin(0) arcsin ( 0) is 0 0. θ = 0 θ = 0. The sine function is positive in the first and second quadrants.

**What are the three trigonometrical ratios of sin Theta?**

We define the three trigonometrical ratios sine θ, cosine θ, and tangent θ as follows (we normally write these in the shortened forms sin θ, cos θ, and tan θ): `sin theta=text(opposite)/text(hypotenuse)` `cos theta =text(adjacent)/text(hypotenuse)` `tan theta =text(opposite)/text(adjacent)`.

### How to find the absolute value of sin(θ) sin( θ) function?

Tap for more steps… The absolute value is the distance between a number and zero. The distance between 0 0 and 1 1 is 1 1. Divide 2 π 2 π by 1 1. The period of the sin(θ) sin ( θ) function is 2π 2 π so values will repeat every 2π 2 π radians in both directions.

### What is the period of the sin(θ) sin function?

The period of the sin(θ) sin ( θ) function is 2π 2 π so values will repeat every 2π 2 π radians in both directions. Consolidate the answers.