How do you find exact value of sin (19pi/12)?

2 Answers
May 11, 2018

264

Explanation:

sin(19π12)=sin(15π12+4π12)
=sin(5π4+π3)
=sin(5π4)cos(π3)+cos(5π4)sin(π3)
=(22)(12)+(22)(32)
=(24)+(64)
=264

May 11, 2018

sin285=14(2+6)

Explanation:

I like to complain that every trig problem uses one of two triangles, 30/60/90 or 45/45/90. This one uses both!

The other answer is fine. Let's do it in degrees here.

19π12×3602π=285

sin285=sin(360+285)=sin(75)=sin75=sin(30+45)

There they are.

sin285=sin(30+45)

=(sin30cos45+cos30sin45)

=((12)(22)+(32)(22))

=14(2+6)