#reference angles

[er-cryptid]

Reference Angle Formulae

Quadrant I -- degree( r ) = degree

Quadrant II -- degree( r ) = 180 - degree -- degree( r ) = pi - degree

Quadrant III -- degree( r ) = degree - 180 -- degree( r ) = degree - pi

Quadrant IV -- degree( r ) = 360 - degree -- degree( r ) = 2(pi) - degree

[pedrihhcrystal]

Crystal Reference Sheet and New Gem Format!

Well, I decided to change its gem to make more sense, I thought the crystal gem was very meaningless because it did not look like a “Crystal”

and thanks to @artifiziell making the table available to make the reference set

I hope you like the new changes ^^

I’ll be back with the comic next Saturday with Chapter 0 of Crystal Origins, a Preview of Chapter 1!

I will improve the quality of the images when I can ^^

[er-cryptid]

Patreon | Ko-fi  

[er-cryptid]

Patreon | Ko-fi  

[er-cryptid]

Patreon | Ko-fi

[er-cryptid]

Patreon | Ko-fi

[math-journal2]

Why do derivative and reference angle notation have to be the same?

TvT

It hurts my eyes.

[lawsofemotion]

Angles in Standard Position and Reference Angles

On a Cartesian plane, you can generate an angle by rotating a ray about the origin. The starting position of the ray, along the positive x-axis, is the initial arm of the angle. The final position, after a rotation about the origin, is the terminal arm of the angle. An angle is said to be an angle in standard position if its vertex is at the origin of a coorinate plane and its initial arm coincides with the positive x-axis. In other words, the vertex must be on the origin and the initial arm must be on the positive x-axis facing east in order to be called an angle in standard position. Initial arm: the arm of an angle in standard position that lies on the x-axis. Terminal arm: the arm of an angle in standard position that meets the initial arm at the origin to form an angle. Angle in standard position: the position of an angle when its initial arm is on the positive x-axis and its vertex is at the origin. Reference angle: an acute angle between the terminal arm and closest x-axis to it. θ: angle θR: reference angle

Quadrant chart:

Example of a reference angle:

x-values are positive in quadrants I and IV. y-values are positive in quadrants I and II. x-values are negative in quadrants II and III. y-values are negative in quadrants III and IV.

Sketch the angle 120° in standard position. The vertex must be on the origin and the initial arm must be on the positive x-axis facing east in order to be called an angle in standard position. So let us first draw the initial arm.

Next we look at the charts and see that north is 90, west is 180 and south is 270. 120 would be over 90 and a little under 180, so the terminal arm must be in quadrant II. It does not need to be perfect angle measure, since the problem said sketch.

Sketch the angle 310° in standard position. The vertex must be on the origin and the initial arm must be on the positive x-axis facing east in order to be called an angle in standard position. So let us first draw the initial arm.

Next we look at the charts and see that north is 90°, west is 180° and south is 270°. 310° would be over 270° and a little under 360°, so the terminal arm must be in quadrant IV. It does not need to be perfect angle measure, since the problem said sketch.

Determine the reference angle for 200°. First, let us draw 200° in standard position.

When we look at the terminal arm, which x-axis is it closer to, 180's or 360's? It seems to be closer to 180's, so to find the reference angle, we subtract 180° from 200° and get 20°. Determine the reference angle for 340°. First, let us draw 340° in standard position.

When we look at the terminal arm, which x-axis is it closer to, 180's or 360's? It seems to be closer to 360's, so to find the reference angle, we subtract 340° from 360° and get 20°. Determine all angles in standard position, 0° < θ < 360°, that have a reference angle of 20°. Let us sketch all the 20° angles that can be formed on the coordinate plane.

For quadrant I, we see that the reference angle is 20°. (0° + 20° = 20°) For quadrant II, we see that the reference angle is 160°. (180° - 20° = 160°) For quadrant III, we see that the reference angle is 200°. (180° + 20° = 200°) For quadrant IV, we see that the reference angle is 340°. (360° - 20° = 340°)