1 Find the exact value of the cosine and sine of the given a

1) Find the exact value of the cosine and sine of the given angle = -43pi/6

2) If sin()=25/5 and pi/2 < < pi, what is cos()?

3) =3 is found in what quadrant and what does ¯ equal to?

Please show the work.

1) = -43pi/6

cos( -43pi/6 ) = cos(43pi/6)

= cos(6pi +7pi/6) = cos(7pi/6)

= cos( pi+pi/6) = -cospi/6

= -sqrt3/2

sin((-43pi/6) = -sin(6pi + 7pi/6)

= -sin(7pi/6)

= -sin(pi + pi/6) = sinpi/6

= 1/2

2) sin()=25/5 and pi/2 < < pi, what is cos()

cos() = sqrt( 1 - sin^2)

= -sqrt( 1- (2sqrt5/5)^2 ) ( cos is -ve in QII as given pi/2 < < pi)

= sqrt( (25 - 20)/25)

= sqrt(5/25) = 1/sqrt5

3) =3 is found in what quadrant and what does ¯ equal to

I understand ¯ = -3 deg.So, it lies in IVrt quadrant and can written as :

¯ = 360 - = 277 deg