Posted March 20, 2017 Hi everyone! I love this question as it deals frequent complex type question. Especially the exact angle part :)! Enjoy! 5 people like this Share this post Link to post Share on other sites

Posted March 20, 2017 Thank you for these amazing math problems! I do really enjoy solving them. Please post more of the challenging Math problems - they are indeed helpful for the preparation. 1 person likes this Share this post Link to post Share on other sites

Posted March 21, 2017 I'm glad to hear that. You are more than welcome to share your answer and discuss your solution with me and other friends. Please do attempt :)! 1 person likes this Share this post Link to post Share on other sites

Posted March 21, 2017 My answer's in the attached file. Answer.docx 1 person likes this Share this post Link to post Share on other sites

Posted March 21, 2017 2 hours ago, SC2Player said: My answer's in the attached file. Answer.docx I can't open your file. Can you make it into PDF? Share this post Link to post Share on other sites

Posted March 22, 2017 Answer in pdf form: Answer.pdf Share this post Link to post Share on other sites

Posted March 22, 2017 5 minutes ago, SC2Player said: Answer in pdf form: Answer.pdf aha, very well done except for some mistake with algebra! Try again for the quadratic substitution and derive a correct answer! (The value was wrong.) Also, for the last part, there could be more than one solution in the second quadrant. Ask me if you get stuck for the second part :)! Share this post Link to post Share on other sites

Posted March 25, 2017 (edited) On 3/22/2017 at 4:03 PM, tutorinseoul said: aha, very well done except for some mistake with algebra! Try again for the quadratic substitution and derive a correct answer! (The value was wrong.) Also, for the last part, there could be more than one solution in the second quadrant. Ask me if you get stuck for the second part :)! Bleh I can't figure out the second part. Can you give me a hint? Also was busy in Korea this week, so couldn't answer your questions alas. Ima do them now (most seem pretty interesting). Edited March 25, 2017 by SC2Player 1 person likes this Share this post Link to post Share on other sites

Posted March 25, 2017 22 minutes ago, SC2Player said: Bleh I can't figure out the second part. Can you give me a hint? Also was busy in Korea this week, so couldn't answer your questions alas. Ima do them now (most seem pretty interesting). Hint: What's cos (9 pi / 10)? 1 person likes this Share this post Link to post Share on other sites

Posted March 25, 2017 25 minutes ago, SC2Player said: Bleh I can't figure out the second part. Can you give me a hint? Also was busy in Korea this week, so couldn't answer your questions alas. Ima do them now (most seem pretty interesting). My triick will be to compare with the closest angle I know! For example, we have to get cos 7pi/10. The closest angle I know is 5pi/10 with exact angle. cos(pi/2) being zero, and since it's decreasing till pi, we know for my y=cos(7pi/10) value it must be bounded by 0 and -1. And then I can compare the value. I will write it up nearly tonight! Been busy in Seoul too lol. Share this post Link to post Share on other sites

Posted March 25, 2017 2 minutes ago, kw0573 said: @SC2Player You skipped the same step in d). It wasn't needed then, but you need the step now. A friend tip is to never skip the same step again. Which step did I skip? Can't figure it out right now. Share this post Link to post Share on other sites

Posted March 25, 2017 1 minute ago, SC2Player said: Which step did I skip? Can't figure it out right now. Keep looking you can find it! On the exam you may have to troubleshoot like this too. Share this post Link to post Share on other sites

Posted March 25, 2017 @SC2Player What did @tutorinseoul meant by the value was wrong, anyways? Share this post Link to post Share on other sites

Posted March 25, 2017 My attempt at finding cos(7pi/10) is in the attached file, but I'm not too sure if it's quite what the question was looking for - feels a bit inefficient tbh. Also had a typo in my original file (had 5sqrt(5) instead of sqrt(5) for some reason), so that's probably where my value was wrong. Answer.pdf 2 people like this Share this post Link to post Share on other sites

Posted March 25, 2017 22 minutes ago, SC2Player said: My attempt at finding cos(7pi/10) is in the attached file, but I'm not too sure if it's quite what the question was looking for - feels a bit inefficient tbh. Also had a typo in my original file (had 5sqrt(5) instead of sqrt(5) for some reason), so that's probably where my value was wrong. Answer.pdf Hey, I've written up my solution; see if you can understand and ask me if there unclear part! Share this post Link to post Share on other sites

Posted March 25, 2017 23 minutes ago, SC2Player said: My attempt at finding cos(7pi/10) is in the attached file, but I'm not too sure if it's quite what the question was looking for - feels a bit inefficient tbh. Also had a typo in my original file (had 5sqrt(5) instead of sqrt(5) for some reason), so that's probably where my value was wrong. Answer.pdf Link http://m.imgur.com/Rxpgevz,rhLNNT5,tO2yIVu 1 person likes this Share this post Link to post Share on other sites

Posted March 25, 2017 (edited) @tutorinseoul I think the testing values is unnecessary. Spoiler cos θ = ± sqrt((5 ± sqrt (5)) / 8) or 0. Note that there are 5 values of cos, and as expected, 5 angles from 0 to pi that satisfy cos (5θ) = 0, which are π/10, 3π/10, π/2, 7π/10, and 9π/10. Since the cos curve is decreasing from 0 to π, cos (7π/10) gets the second smallest (second least positive) value, which is -sqrt((5 - sqrt (5)) / 8). Therefore in finding values of cos π/10, it is also important to state that because cos π/10 >cos 3π/10, it is the largest of the 5 cos values. @SC2Player. You are right. The typo you made mistakenly allowed you to reject 5 - 5sqrt (5)) / 8 as a value of cos^{2}θ because it is negative. It is always important to make sure the roots you reject actually can be rejected. Edited March 25, 2017 by kw0573 1 person likes this Share this post Link to post Share on other sites

Posted March 25, 2017 1 hour ago, kw0573 said: @tutorinseoul I think the testing values is unnecessary. Reveal hidden contents cos θ = ± sqrt((5 ± sqrt (5)) / 8) or 0. Note that there are 5 values of cos, and as expected, 5 angles from 0 to pi that satisfy cos (5θ) = 0, which are π/10, 3π/10, π/2, 7π/10, and 9π/10. Since the cos curve is decreasing from 0 to π, cos (7π/10) gets the second smallest (second least positive) value, which is -sqrt((5 - sqrt (5)) / 8). Therefore in finding values of cos π/10, it is also important to state that because cos π/10 >cos 3π/10, it is the largest of the 5 cos values. @SC2Player. You are right. The typo you made mistakenly allowed you to reject 5 - 5sqrt (5)) / 8 as a value of cos^{2}θ because it is negative. It is always important to make sure the roots you reject actually can be rejected. You are right :)! I just ne d to think of pi, 3pi, 5 pi and 7pi over pi for my solutions as they only make the equation to be zero when they were substituted into cos 5x. Just wanted to use different approach :)! Thank you for your comments. Share this post Link to post Share on other sites