In Exercises 17 you are asked to find the sine cosine and ta

In Exercises 1-7 you are asked to find the sine, cosine and tangent of the double angle 2, as well as the quadrant 2 sits in, based on the given information on . Use exact values.  Show work

1. cos = 8/17 , in QuadrantIV.

2. sin =7/25 , in QuadrantIII.

Solution

1. cos = 8/17 , in QuadrantIV.

sin = sqrt(1 -(8/17)^2) = -15/17     ( sin is -ve in IVrt quad)

sin2 = 2sincos = 2(8/17)(-15/17) = - 240/289

cos2 = 2cos^2 -1 = 2(8/17)^2 -1 = -161/289

tan2 = sin2/cos2 = 240/161

2. sin =7/25 , in QuadrantIII

cos = sqrt( 1 -sin^2) = sqrt( 1 -(7/25)^2) = - 24/25    (cos is -ve in QIII)

sin2 = 2sincos = 2*(-7/25)(-24/25) = 336/625

cos2 = 2cos^2 -1 = 2(-24/25)^2 -1 = 527/625

tan2 = sin2/cos2 = 336/527