trig fourmulas and proofs

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March 3rd 2009, 05:17 PM
Heather10

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!
March 3rd 2009, 05:42 PM
mathaddict

Quote:

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 :

$<br /> Sin23 cos37 + cos23 sin37=sin(23+37)=sin60=\frac{\sqrt{3}}{2}<br />$
March 3rd 2009, 09:53 PM
mathaddict

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 .