Find the exact value of the expression sin Need Help Master

Find the exact value of the expression. sin()() Need Help? Master 13. -1 points SAg Trig4 7.2.055.MI. Evaluate the expression under the given conditions cos() = 3, cos(8-); in Quadrant lv, tan(p)--V3, pin Quadrant 11 Need Help? Waich Mast Master It 14. a-1 points SAgTrig4 7.2.057. Evaluate the expression under the given conditions. sin( + ); sin()-, in Quadrant 1, cos(p)-- in Quadrant 11 Need Help? Watch esc : Fr F2 F3 FS

Solution

let cos^-1 (5/6) = a

cos a = 5/6

sin a = sqrt 11 / 6

tan^-1 (1/4) = b

tan b = 1/4

sin b = 1 / sqrt 17

cos b = 4 / sqrt 17

so our expression now is

sin ( a - b ) = sin a cos b - cos a sin b

= sqrt 11/ 6 * 4 / sqrt 17 - 5/6 * 1 / sqrt 17

= 4 sqrt 11 / 6 sqrt 17 - 5 / 6sqrt 17

= ( 4 sqrt 11 - 5 ) / ( 6 sqrt 17 )