# Thread: trig fourmulas and proofs

1. ## trig fourmulas and proofs

Use the addition formulas to find the exact value of the given expression
1) Cos 11(pi)/12

2) Sin23 cos37 + cos23 sin37

FORMULAS:
sin(u +/- v) = (sin u cos v +\- cos u sin v)
cos(u +/- v) = (cos u cos v -\+ sin u sin v)
tan(u +/- v) = (tan u +\- tan v) / (1 -\+ tan u tan v)

My teacher gave this worksheet and gave the answers and is grading on the work and process... unfortunately i was sick the day we learned how to do these. Any help AND explanation would be greatly apreciated!

2. Originally Posted by Heather10
Use the addition formulas to find the exact value of the given expression
1) Cos 11(pi)/12

2) Sin23 cos37 + cos23 sin37

FORMULAS:
sin(u +/- v) = (sin u cos v +\- cos u sin v)
cos(u +/- v) = (cos u cos v -\+ sin u sin v)
tan(u +/- v) = (tan u +\- tan v) / (1 -\+ tan u tan v)

My teacher gave this worksheet and gave the answers and is grading on the work and process... unfortunately i was sick the day we learned how to do these. Any help AND explanation would be greatly apreciated!
(1) error made, see below post

(2)Use the sin addition formula :

$
Sin23 cos37 + cos23 sin37=sin(23+37)=sin60=\frac{\sqrt{3}}{2}
$

3. Sorry i made a mistake for (1)

$cos\frac{11\pi}{12}=cos\frac{11}{12}(180)=cos165=-cos15$

Perhaps you are not allowed to use the calculator to do this :

$-cos15=-cos\frac{1}{2}(30)$

Use this identity :

$cos\frac{a}{2}=\sqrt{\frac{1+cosa}{2}}$ where a=30 .