Question

find the reference angle, quadrant, and rotational angle for the point (3,-8)

Answer 1

x = 3, so to the right of origin
y = -8 so below the origin
That is quadrant IV

tan A = -8/3
where A is angle below the +x axis
so 360 - A

Answer 2

Many students (and teachers) make this more difficult than it has to be.
Step1 : plot the given point, join it to the origin. Using this as the hypotenuse, draw an altitude <b>to the x-axis>/b> and complete the right angled triangle.
Step 2: Unless you are already in the first quadrant, construct a similar triangle in the first quadrant
(everything will now be positive)
Step 3: let tan Ø = opposite/hypotenuse
use your calculator to find Ø ( the 2nd function tan key)

Ø is your reference angle or often called "the angle in standard position"

to find the rotational actual angle:
in quad I --- your reference angle is it
in quad II -- 180° - Ø
in quad III -- 180° + Ø
in quad IV -- 360° - Ø

follow these steps, and let me know how you did.</b>

Answer 3

oops, forgot to turn off my "bold" text.

Many students (and teachers) make this more difficult than it has to be.
Step1 : plot the given point, join it to the origin. Using this as the hypotenuse, draw an altitude <b>to the x-axis</b> and complete the right angled triangle.
Step 2: Unless you are already in the first quadrant, construct a similar triangle in the first quadrant
(everything will now be positive)
Step 3: let tan Ø = opposite/hypotenuse
use your calculator to find Ø ( the 2nd function tan key)

Ø is your reference angle or often called "the angle in standard position"

to find the rotational actual angle:
in quad I --- your reference angle is it
in quad II -- 180° - Ø
in quad III -- 180° + Ø
in quad IV -- 360° - Ø

follow these steps, and let me know how you did.

Answer 4

eh ?
tan Ø = opposite/hypotenuse
LOL

Answer 5

Damon, mea culpa.

"old-timers" setting in.

Answer 6

:)
anyway
tan Ø = opposite/adjacent

Answer 7

I get 58 degrees below x axis
360 - 58 = 302 counterclockwise from x axis