Use the given information to find the values of sin 2theta c

Use the given information to find the values of sin 2theta, cos 2theta, and tan 2theta 2theta sin theta = 24/25, The terminal side of 6 ties in quadrant III

Solution

sin = -24/25 is in QIII

so by sin^2 +cos^2 =1 we have to find cos value

cos^2 = 1 - (-24/25)^2

cos^2 = (625-576)/625

cos =-7/25 (since is in QIII)

i)

sin2 = 2sin.cos

= 2.(-24/25).(-7/25)

= 336/625

ii).cos2 = cos^2 -sin^2

= (-7/25)^2 - (-24/25)^2

= 49/225 - 576/625

= -527/625

iii)

tan2 =sin(2)/cos(2) = 336/-527

= -336/527