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Question
I do not understand how to solve: 2 cos^2 x = 13 sin x - 5 given that 0 </= x < 2pi.
Thank you very much for your help!
Hi Keli,
Well, I won't show you how to do the whole thing, but I will give you a nice hint.
You know that cos^2x + sin^2x = 1
so cos^2z = 1 - sin^2x
so the equation is the same thing as...
2(1 - sin^2x) = 13sinx - 5
now if you substitute that y = sinx.
we get...
2(1 - y^2) = 13y - 5
now you should solve this on your own and once you have y, solve for x by saying
y = sinx.
Ask again if you need further help,
Robi
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Answers by Expert:
Robi Bhattacharjee
Expertise
I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.
Experience
I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).
Organizations
I am in the San Diego Math Circle
Education/Credentials
I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.
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