5 13 16 Find sin2r if secx and x in QIII Solutionsecx 135 se

5 13 16. Find sin(2r) if secx- and x in QIII.

Solution

secx =-13/5

secx =1/cosx

=>cosx=1/secx

=>cosx=1/(-13/5)

=>cosx =-5/13

adjacent side =5,hypotenuse =13

opposite side²+adjacentside²=hypotenuse²

opposite side²+5²=13²

opposite side²+25=169

opposite side²=144

opposite side=12

in QIII sinx is negative

sinx =oppositeside/hypotenuse

sinx =-12/13

sin2x =2sinx cosx

sin2x =2(-12/13)(-5/13)

sin2x =120/169