Question

The exact value of cos5pi/12 is?

Answer 1

Our Half-Angle Identity for Cosine tells us:\[\Large\rm \cos\left(\frac{\color{orangered}{\theta}}{2}\right)=\sqrt{\frac{1+\cos(2\color{orangered}{\theta})}{2}}\]

Answer 2

Applying this to our problem:\[\Large\rm \cos\left(\frac{5\pi}{12}\right)=\cos\left(\frac{\color{orangered}{5\pi/6}}{2}\right)=\sqrt{\frac{1+\cos(2\cdot\color{orangered}{5\pi/6})}{2}}\]

Answer 3

Understand how I broke down the 5pi/12? :o

Answer 4

@zepdrix Wait Yes I think its B then

Answer 5

With the subtraction under the root? Hmmm... <.<

Answer 6

\[\huge \bf \cos \frac{5 \pi}{12}=cos 75^o\]
\[\huge \bf \cos 75^o=\cos (90-15)^o\]
remember :-
\[\huge \bf \cos(90- \theta)=\sin \theta\]

so, we get
\[\huge \bf \cos(90-15)^o=\sin 15^o\]

Answer 7

do you know the value of sin 15 degree? @Clarke11

Answer 8

@zepdrix well i know that A and D are out of the question so

Answer 9

\[\Large\rm \cos\left(\frac{10\pi}{6}\right)=\cos\left(\frac{5\pi}{3}\right)\]That should be giving us a positive value, yes? :d

Answer 10

@Clarke11 remember you have to remember its value :-
\[\huge \bf \sin 15^o=\frac{\sqrt{3}-1}{2\sqrt{2}}\]

Answer 11

@zepdrix Im guessing it has to be a positive value because where would the negative some from anyway

Answer 12

therefore,option B is correct answer.

Answer 13

Well if we had ended up with a cos(4pi/3) it could be negative under the root! :)
It just didn't work out that way.
cos(5pi/3) is in quadrant 4, cosine is positive there.

Answer 14

@zepdrix your method is too long

Answer 15

Are you kidding?
You still have to apply the Half-Angle Identity when you get to sin(15).

Answer 16

Or are you just remembering some weird formula?

Answer 17

your method requires some formula but my method is basic trig method

Answer 18

sin(15) is NOT a basic angle that you're expected to remember.

Answer 19

@zepdrix your method is also correct but in compare with my method,my method is so basic than your's

Answer 20

I mean another option would be to go from your cos(90-15) and apply the cosine angle sum identity.

Answer 21

no you're relies on memorizing a very very obscure sine angle.

Answer 22

yours*

Answer 23

@mayankdevnani and @zepdrix I have one more question for both of you because im really bad at trig if you guys dont mind lmao

Given sinx=3/5 and x is in quadrant 2 what is the value of tan x/2

Answer 24

remember :-
\[\huge \bf \sin \theta=\frac{3}{5}=\sin 37^o\]
\[\huge \bf \sin \theta=\frac{4}{5}=\sin 53 ^o\]