Question 1194932: please help me solve sin(2cos^-1(2v))
Answer by ikleyn(52871)   (Show Source):
You can put this solution on YOUR website! .
please help me solve sin(2cos^-1(2v))
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They want you find sin(2a), given that cos(a) = 2v and 0 <= a <  .
Apply the formula for the sine of doubled argument
sin(2a) = 2sin(a)*cos(a).
In this formula, you are just given that cos(a) = 2v; but you still don't know sin(a).
You can easy find the expression for sin(a): it is
sin(a) =  =  =  .
Notice here, that I use the positive square root for sine,
since the sine function is positive for 0 <= a < .
THEREFORE,
sin(2cos^-1(2v)) = 2*sin(a)*cos(a) =  =  .
ANSWER. sin(2cos^-1(2v)) = .
Solved.
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I know that for many students, the entire formulation of such problems is often non-understandable,
as well as it is non-understandable thing where and how to start.
Try to start using the words " They want you find . . . ", as I started my solution.
It may happen that your internal voice will give then a que to you on how to continue.
For such problems, these words " They want you find . . . " are magic words (like a mantra)
and often help to start and to solve the problem to the end.
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To see other similar solved problems on calculating trig functions, look into 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".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.
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