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ash2326Best ResponseYou've already chosen the best response.1
@IloveCharlie what's 30' in degrees?
 one year ago

GOODMANBest ResponseYou've already chosen the best response.1
Divide 30 seconds by 60. After that, add it to 67. Then take the cosine of it all.
 one year ago

IloveCharlieBest ResponseYou've already chosen the best response.0
Hmmm... I got .382. Can you please confirm?
 one year ago

ash2326Best ResponseYou've already chosen the best response.1
yeah, it's right but could you use calculator for this? @IloveCharlie
 one year ago

IloveCharlieBest ResponseYou've already chosen the best response.0
I just don't know which one it matches up with :/ From the options given
 one year ago

IloveCharlieBest ResponseYou've already chosen the best response.0
Whoa @jim_thompson5910 you're typing a lot
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
Yes it's a lot, but it at least gives you the exact answer 67 degrees 30' = 67 degrees + 30/60 = 67+0.5 = 67.5 degress Notice how 2*67.5 = 135 and \[\Large \cos(135) = \frac{\sqrt{2}}{2}\] (using the unit circle) Now turn to the identity \[\Large \cos(x) = \sqrt{ \frac{ \cos(2x) + 1 }{2} }\] If we let x = 67.5, then \[\Large \cos(x) = \sqrt{ \frac{ \cos(2x) + 1 }{2} }\] \[\Large \cos(67.5) = \sqrt{ \frac{ \cos(2*67.5) + 1 }{2} }\] \[\Large \cos(67.5) = \sqrt{ \frac{ \cos(135) + 1 }{2} }\] \[\Large \cos(67.5) = \sqrt{ \frac{ \frac{\sqrt{2}}{2} + 1 }{2} }\] \[\Large \cos(67.5) = \sqrt{ \frac{ \frac{\sqrt{2}}{2} + \frac{2}{2} }{2} }\] \[\Large \cos(67.5) = \sqrt{ \frac{ \frac{\sqrt{2}+2}{2} }{2} }\] \[\Large \cos(67.5) = \sqrt{ \frac{ \frac{2\sqrt{2}}{2} }{2} }\] \[\Large \cos(67.5) = \sqrt{ \left( \frac{2\sqrt{2}}{2} \right)\left(\frac{1}{2}\right) }\] \[\Large \cos(67.5) = \sqrt{ \frac{(2\sqrt{2})*1}{2*2} }\] \[\Large \cos(67.5) = \sqrt{ \frac{2\sqrt{2}}{4} }\] \[\Large \cos(67.5) = \frac{\sqrt{2\sqrt{2}}}{\sqrt{4}}\] \[\Large \cos(67.5) = \frac{\sqrt{2\sqrt{2}}}{2}\]
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
sry i had a typo, but i fixed it
 one year ago

IloveCharlieBest ResponseYou've already chosen the best response.0
Wow, thanks so much for the awesome step by step explanation! Really helps!
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
you're welcome
 one year ago
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