Question

Find the exact values of the sine, cosine, and tangent of the angle.

19π/12 = 11π/6 - π/4

Answer 1

kind of weird question set up.
Like asking:Find the exact values of the sine, cosine, and tangent of the angle.
285deg = 330deg - 45deg

What angle do you want sin cos and tan of? if 285, the use a calculator and plug it in.

Answer 2

or subtract 19π/12 from each side to get 0deg and find sin, cos and tan of that?

Answer 3

\[\sin \frac{ 19\pi }{ 12 }=\sin \left( \frac{ 11\pi }{6 }-\frac{ \pi }{ 4 } \right)\]
\[=\sin \frac{ 11\pi }{6 }\cos \frac{ \pi }{4 }-\cos \frac{ 11\pi }{6 }\sin \frac{ \pi }{4 }\]

Answer 4

\[\sin \frac{ 11\pi }{6 }=\sin \left( 2\pi-\frac{ \pi }{6 } \right)=-\sin \frac{ \pi }{ 6 }=-\frac{ 1 }{ 2 }\]
\[\cos \frac{ 11\pi }{ 6 }=\cos \left( 2\pi-\frac{ \pi }{ 6 } \right)=\cos \frac{ \pi }{6 }=\frac{ \sqrt{3} }{2 }\]
\[\tan \frac{ 11\pi }{ 6 }=\tan \left( 2\pi-\frac{ \pi }{6 } \right)=-\tan \frac{ \pi }{ 6 }=-\frac{ \sin \frac{ \pi }{6 } }{\cos \frac{ \pi }{ 6 } }=-\frac{ 1 }{\sqrt{3} }\]

Answer 5

\[\sin \frac{ \pi }{ 4 }=\frac{ 1 }{\sqrt{2} },\cos \frac{ \pi }{ 4 }=\frac{ 1 }{ \sqrt{2} },\tan \frac{ \pi }{ 4 }=1 \]

Answer 6

\[\cos \left( A-B \right)=\cos A \cos B+\sin A \sin B\]
\[\tan \left( A-B \right)=\frac{ \tan A-\tan B }{ 1+\tan A \tan B }\]

Answer 7

GOT IT. THANKS MAN!

Answer 8

yw