Question

MEDAL* find the exact value of the expression: sin(3pi/4+5pi/6)

Answer 1

Find the exact value of the expression:
sin (3pi/4) cos (5pi/6) - cos(3pi/4) sin (5pi/6)
**
Addition formula for sin function:
sin(s-t)=sin s cos t - cos s sin t
For given function:

s=3π/4
t=5π/6
..
sin (3π/4) cos (5π/6) - cos(3π/4) sin (5π/6)
=sin(s-t)
=sin(3π/4-5π/6)
=sin(9π/12-10π/12)
=sin(-π/12)=-0.2588

Answer 2

d

Answer 3

\[\sin \left( \frac{ 3\pi }{ 4 }+\frac{ 5\pi }{6 } \right)=\sin \left( \frac{ 9\pi+10\pi }{12 } \right)=\sin \frac{ 19\pi }{ 12 }\]
\[=\sin \left( \pi+\frac{ 7\pi }{12 } \right)=-\sin \frac{ 7\pi }{ 12 }\]
\[=-\sin \left( \frac{ 4\pi+3\pi }{12 } \right)=-\sin \left( \frac{4\pi }{ 12 }+\frac{ 3\pi }{12 } \right)=-\sin \left( \frac{ \pi }{ 3 }+\frac{ \pi }{ 4 } \right)\]
\[=-\left[ \sin \frac{ \pi }{ 3 } \cos \frac{ \pi }{ 4 } +\cos \frac{ \pi }{3 } \sin \frac{ \pi }{4 } \right]\]
\[=-\left[ \frac{ \sqrt{3} }{2 }*\frac{ 1 }{ \sqrt{2} }+\frac{ 1 }{2 } *\frac{ 1 }{\sqrt{2} }\right]=-\frac{ \sqrt{3}+1 }{ 2\sqrt{2} }=-\frac{ \sqrt{6}+\sqrt{2} }{ 4 }\]
\[=-\frac{2.449+1.414 }{4 }=-\frac{ 3.863 }{ 4 }=-0.9675\]

Answer 4

correction -0.96575