Question

find the exact value of the expression

Cos(sin^-1 square root(3) divided by 2)

Answer 1

Where is the sine function equal to (square root(3) divided by 2) in Quadrant One?

Answer 2

By where, I mean what angle? Are we working in degrees or radians or does it matter?

Answer 3

radians

Answer 4

Take a look at the attached table of selected trig values.

Answer 5

@NorthGeorgiaBoy17

Answer 6

im lost now, so do i plug in one of those values for cos and sin?

Answer 7

@NorthGeorgiaBoy17 Look at the attached table. I wrote on it. Look at the section I highlighted.

Answer 8

so i do cos(60)?

Answer 9

From the table, the sine is (square root(3) divided by 2) at pi/3 radians or 60 degrees.

Answer 10

Yes, @NorthGeorgiaBoy17

Answer 11

And, that value is ? @NorthGeorgiaBoy17

Answer 12

\[\cos(\sin^{-1}(\frac{ \sqrt3 }{ 2 }))=\cos \left( \frac{ \pi }{ 3 } \right)\]Do you know how I got that? I got that because in order to solve the whole thing, we must first evaluate the expression arcsin(sqrt(3)/2) in the brackets. We know that sin^-1(sqrt(3)/2) is the same as saying for what value does sin = sqrt(3)/2? So we write it more formally like this:\[y=\sin^{-1}x \implies \sin y = x\]We know x = sqrt(3)/2, so we solve for y by finding for what value is the sine graph equal to sqrt(3)/2.\[\sin^{-1}x=y \implies \sin y=x \rightarrow \sin^{-1}\left( \frac{ \sqrt3 }{ 2 } \right) \implies \sin y = \frac{ \sqrt3 }{ 2 } \implies y=\frac{ \pi }{ 3 }\]So now can, can you evaluate cos(pi/3)?

@NorthGeorgiaBoy17

Answer 13

And, that value is ? @NorthGeorgiaBoy17

Answer 14

so the answer is 1/2 ?!

Answer 15

Yes!

Answer 16

Yes.

Answer 17

Good job.

Answer 18

thanks friends

Answer 19

@NorthGeorgiaBoy17

I see that you may be new to OpenStudy. Welcome.

Answer 20

yes i am, thank you!

Answer 21

Well since you're new, I should also tell you that you may give a helpful answer a medal by clicking "Best Response" on the answer.

@NorthGeorgiaBoy17

Answer 22

@Directrix I'll take care of you lol.

Answer 23

That's the spirit. Thanks.

Answer 24

And I just didn't give an answer. I thoroughly explained and left it on him to generate the answer =[

Answer 25

And I wasn't indirectly asking for a medal, I swear lol...@Directrix

Answer 26

directrix ill give you a medal too if you just type anything on the question i just poster

Answer 27

posted

Answer 28

becuase yall both helped and id like to be nice.

Answer 29

@genius12
Well, OS is somewhat like an online game. Earning medals or being awarded a medal for helping is tantamount to a "thank you." New users do not know that. If the Ambassadors would gently explain that, then the new users would understand how they can get quicker help.
After all, we are human and like the medals. Just my opinon.

Answer 30

@NorthGeorgiaBoy17 @genius12 is a caring OpenStudier and solved the medal issue. So, no worries. It's all okay.

Answer 31

okay! i didnt mean to offend anyone! hope we're all good.

Answer 32

We are all good. Nobody is offended.

Answer 33

okay good!! thanks so much for you're help! i hope you help me again sometime:)