Why are reference angles always positive?

The reference angle is always positive. In other words, the reference angle is an angle being sandwiched by the terminal side and the x-axis. It must be less than 90 degree, and always positive.

What to the X and Y coordinates on the unit circle represent?

A unit circle has a center at (0,0) and radius 1 . In a unit circle, the length of the intercepted arc is equal to the radian measure of the central angle 1. Let (x,y) be the endpoint on the unit circle of an arc of arc length s. The (x,y) coordinates of this point can be described as functions of the angle.

Why is the x-axis the cos theta?

Because when the trigonometric ratios are first introduced, the base of a right-angled triangle is almost always taken as horizontal, and cos(theta) is taken as base/hypotenuse. And it it is easier for the pupil to identify the x-axis as the horizontal direction.

Why is the hypotenuse always positive in the unit circle?

moving along a given circle, the x-value and y-value move from positive to negative and back, but each vanishes as it passes from positive to negative and back. The hypotenuse of the triangle never vanishes; so to be continuous, its sign must remain positive.

How do you find positive and negative Coterminal angles?

To find a positive and a negative angle coterminal with a given angle, you can add and subtract 360°if the angle is measured in degrees or 2π if the angle is measured in radians. Example 1: Find a positive and a negative angle coterminal with a 55°angle. A −305°angle and a 415°angle are coterminal with a 55°angle.

Is x-axis sin or cos?

The x-coordinate is the value of cos θ, and the y-coordinate is the value of sin θ. The other points are reflections of the first point over the x-axis, the y-axis, or both.

Why is the radius always positive?

Firstly, radius is a distance and distances can never be negative. Secondly, rwhere (a,b) is the center of the circle, as you can see ‘r’ is a squared term which is always positive.

Why is C positive in the Pythagorean Theorem?

Explanation: Because it is the length of the side of a triangle and the length of a real object cannot be negative.

What is a function of a positive acute angle?

The positive acute angle θ will be the angle created between the x -axis and the hypotenuse of the triangle. The lengths of the two legs of the triangle will be the x and y coordinates of a point in the first quadrant.

Is an acute angle positive or negative?

The coterminal angles of 480°, 840°, and 240° all share the same principal angle of 120°. The related acute angle is the angle formed by the terminal arm of an angle in standard position and the x-axis. The related acute angle is always positive and lies between 0° and 90°.

How do you label the x-axis and the Y-axis?

If both variables are just observed, but you suspect a casual relationship between them, put “the cause” on the x-axis. If you are would like to make predictions of one variable based on the other, put the one you’re predicting on the y-axis and what you’re basing it on on the x-axis. Regardless of what you do, label axes clearly.$endgroup$

How do you title a graph with X and y axis?

Titling the Graph. The proper form for a graph title is “y-axis variable vs. x-axis variable.”. For example, if you were comparing the the amount of fertilizer to how much a plant grew, the amount of fertilizer would be the independent, or x-axis variable and the growth would be the dependent, or y-axis variable.

Which variable should you put on the x-axis?

When using a graph to represent data, determining which variable to put on the x-axis is important because it should be the independent variable. The independent variable is the one that affects the other.

What is the angle from the positive x axis to zero?

The angle is 0° to 360° measured as a counter-clockwise rotation from the positive x axis. The angle is 0° to +180° measured as a counter-clockwise rotation from the positive x axis,