Question

) Find the exact value: cos(7pi/12)
Part I: Find two common angles that either add up to or differ by 7pi/12. Rewrite this problem as the cosine of either a sum or a difference of those two angles.
Part II: Evaluate the expression.

2) tan(17pi/12)
Part I: Find two common angles that either add up to or differ by 17pi/12.
Part II: Evaluate.

3) sin(195 degrees)
Part I: pretty much the same as above
Part II: Evaluate.

4) cot(15 degrees)
Part I: Find two common angles that differ by 15 degrees. Rewrite this problem as the cotangent of a difference of those two angles.
Part II: Evaluate the expression.

Answer 1

do you know how to do it?

Answer 2

1.
\[\frac{ 7 \pi }{12 }=\frac{ \pi }{ 3 }+\frac{ \pi }{ 4 }\]
\[\cos (\frac{ 7\pi }{ 12})=\cos (\frac{ \pi }{ 3 }+\frac{ \pi }{ 4})\]
\[=\cos \frac{ \pi }{ 3 }\cos \frac{ \pi }{ 4 }-\sin \frac{ \pi }{ 3 }\sin \frac{ \pi }{ 4}\]
=?

Answer 3

2.
\[\frac{ 17 \pi }{12 }=2\pi-\frac{ 7\pi }{ 12 }\]

Answer 4

\[\tan (\frac{ 17\pi }{ 12 })=\tan (2\pi-\frac{ 7\pi }{ 12})=-\tan (\frac{ 7 \pi }{12})\]

Answer 5

2.
\[=-\tan (\frac{ \pi }{ 3 }+\frac{ \pi }{ 4})\]
\[=-\frac{ \tan \frac{ \pi }{ 3 }+\tan \frac{ \pi }{ 4} }{ 1-\tan \frac{ \pi }{ 3 } \tan \frac{ \pi }{ 4 }}\]
=?
3.

\[\sin (195)=\sin (180+15)=-\sin 15=-\sin (45-30)\]
\[=-(\sin45\cos30-\cos45\sin30)=?\]

Answer 6

4.
\[\cot15=\cot(90-75)=\tan 75\]
\[=\tan (45+30)\]
\[=\frac{ \tan 45+\tan30 }{ 1-\tan 45 \tan 30 }=?\]
or
4.
\[\cot15=\frac{ 1 }{ \tan 15 }=\frac{ 1 }{ \tan (45-30)}\]
\[=\frac{ 1 }{\frac{ \tan45-\tan30 }{ 1+\tan 45\tan30 } }\]
\[=\frac{ 1+\tan45 \tan 30 }{ \tan45-\tan30 }=?\]