Answer:
1) The angle would be 150 degrees
a) coordinates would be ( [tex]-\frac{\sqrt{3}}{2}[/tex], [tex]\frac{1}{2}[/tex] )
b) Trigonometric ratios:
sin: [tex]\frac{1}{2}[/tex]
cos: [tex]-\frac{\sqrt{3}}{2}[/tex]
tan: [tex]-\frac{\sqrt{3}}{3}[/tex]
csc: 2,
sec: [tex]-\frac{2\sqrt{3}}{3}[/tex]
cot: [tex]\sqrt{3}[/tex]
Explanation:
[tex]\frac{17\pi }{6}[/tex] simplifys to [tex]\frac{5\pi }{6}[/tex] which has a reference angle of [tex]\frac{\pi }{6}[/tex]. We can take the coordinates of [tex]\frac{\pi }{6}[/tex] and make the x value negative to find the correct coordiantes. Then, using those coordinates, plug the into the trigonomic equations.
For example, sin in opposite/hypotenuse. So sin = 1/2 divided by 1. Then you can find the rest of the equations that way.
cos= adjacent/hypotenuse
tan= sin/cos
csc= hypotenuse/opposite
sec= hypotenuse/adjacent
cot= cos/sin
