For each angle listed in the table below select the letter o

For each angle listed in the table below, select the letter of the corresponding point on the unit circle, the value of the x-coordinate of the point, and the value of the y-coordinate of the point. Round the coordinates of the point to 3 decimal places. Don\'t enter sin or cos. (You must approximate your answers.)

Solution

The points A,B,C,D,E,F are all on the circumference of a unit circle so each of lines connecting the center of the circle to these points = 1. Sin = Perpendicula/hypotenuse = y-coordinate/1 =y-coordinate; cos = base/hypotenuse = x-coordinate/1 = x- coordinate.

Angle

Point

x-coordinate

y-coordinate

Reason

-400⁰

F

0 .766

-0.643

-400⁰ = -360⁰ – 40⁰ = -40⁰; Sin (-40⁰)=-0.643;cos(-40⁰ )= 0.766

45⁰

A

2/2

2/2

The line from the center of the circle to A bisects the angle of 90⁰ sin(45) = cos(45) = 2/2

800⁰

B

0.174

0.985

800⁰ = 2*360⁰ + 80⁰ ; sin(80⁰) =0.985 cos(80⁰) = 0.174

-150⁰

D

-3/2

-1/2

-150⁰ = - (180⁰ – 30⁰); sin(-150⁰)= -1/2 cos(-150⁰)= -3/2

150⁰

C

-3/2

1/2

150⁰ = (180⁰ – 30⁰); sin(150⁰)=1/2 cos(150⁰)= -3/2

250⁰

E

-0.342

-0.940

250⁰ = ( 180⁰ + 70⁰ ) sin(250⁰)= -0.940 cos(250⁰)= -0.342

Angle	Point	x-coordinate	y-coordinate	Reason
-4000	F	0 .766	-0.643	-4000 = -3600 – 400 = -400; Sin (-400)=-0.643;cos(-400 )= 0.766
450	A	2/2	2/2	The line from the center of the circle to A bisects the angle of 900 sin(45) = cos(45) = 2/2
8000	B	0.174	0.985	8000 = 2*3600 + 800 ; sin(800) =0.985 cos(800) = 0.174
-1500	D	-3/2	-1/2	-1500 = - (1800 – 300); sin(-1500)= -1/2 cos(-1500)= -3/2
1500	C	-3/2	1/2	1500 = (1800 – 300); sin(1500)=1/2 cos(1500)= -3/2
2500	E	-0.342	-0.940	2500 = ( 1800 + 700 ) sin(2500)= -0.940 cos(2500)= -0.342