SOLUTION: determine the exact value of sin2ø given that cosø=-12/13 and &#960;<ø<3&#960;/2 without determine the value of ø.

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Question 1061183: determine the exact value of sin2ø given that cosø=-12/13 and π<ø<3π/2 without determine the value of ø.
Found 2 solutions by ikleyn, jim_thompson5910:
Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
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determine the exact value of sin2ø given that cosø=-12/13 and π<ø<3π/2 without determine the value of ø.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

If   =  and  <  <= , then

 =  =  =  =  =  = .

The sign  "-"  was taken at  sqrt,  because sine is negative in QIII.


Then 

 =  =  = .

Solved.


For many other similar solved problems see the lessons
    - Calculating trigonometric functions of angles
    - Advanced problems on calculating trigonometric functions of angles
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Trigonometry: Solved problems".



Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Given:


Let's use this to find


Pythagorean Identity:








Replace with (see "given" above)























See note below





Note: is between and which means is in quadrant 3. This is where is negative. So the "plus/minus" usually associated with the square root is dropped in favor of just a minus.


-------------------------------------------------------


We now have enough to compute using the double angle identity


Using that identity, we get





Plug in the known info








-------------------------------------------------------


The final answer is

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