find the reference angle, quadrant, and rotational angle for the point (3,-8)
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
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 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.
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 to the x-axis 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.
eh ?
tan Ø = opposite/hypotenuse
LOL
Damon, mea culpa.
"old-timers" setting in.
:)
anyway
tan Ø = opposite/adjacent
I get 58 degrees below x axis
360 - 58 = 302 counterclockwise from x axis