5. arc length = radius x central angle in radians
arc length = 28 x 3Ï€/4 = 21Ï€
answer: (21Ï€) cm
6. You are right. Quadrant 1 features points where both the x coordinate and the y coordinate are positive. Cosine and sine are basically special coordinates.
7. We need to find the tan(2Ï€/3). The hint is quite bad I must say because you need to find the sine and cosine of an angle to find tangent. Okay, back to the problem.
tan(2Ï€/3) = sin(2Ï€/3)/cos(2Ï€/3)
We know π/3 to be a special angle on the unit circle. It has a cosine of 1/2 and a sine of [tex]\frac{\sqrt{3} }{2}[/tex]. Because we know this, its partner in quadrant 2 (2π/3) will have a cosine of -1/2 and a sine of [tex]\frac{\sqrt{3} }{2}[/tex].
tan(2π/3) =  [tex]\frac{\sqrt{3} }{2}[/tex] ÷ -1/2= -√3
answer: -√3
8. Both angles are special angles so...
2cos(π/6) - 2tan(π/3) = 2([tex]\frac{\sqrt{3} }{2}[/tex]) - 2([tex]\frac{\sqrt{3} }{2}[/tex] ÷ 1/2) = √3 - 2√3 = -√3 (ok what a coincidence)
answer: -√3
