#### Archived

This topic is now archived and is closed to further replies.

# sin(arc cos(-0.2))=?

This topic is 5913 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Could someone tell me how to solve this: sin(arc cos(-0.2))=?

##### Share on other sites
Use a calculator?

On a calculator you should have a cos-1 button. Put in -0.2, and press it (or the other way round, depending on what your calculator likes). Then press sin and you have your answer. I think.

Miles]

[edited by - Miles Clapham on September 10, 2002 5:51:22 PM]

##### Share on other sites
I know that But how do you solve this without a calculator?

##### Share on other sites
Whipping out my handy Ti-83+, I see that the answer is 0.9797958971...

Of course, physically finding the answer would be more complicated...

_____________________________

And the Phoenix shall rise from the ashes...

--Thunder_Hawk -- ¦þ
______________________________

##### Share on other sites

Sin (arc cos (-0.2) = x

Apply arc sin to both sides of equation , this becomes

Arc cos (-0.2) = arc sin (x) …………………… because arc sin (sin) = 1

Arc cos (-0.2) means “angle whose cosine is - 0.2” ,

from calculator arc cos (-0.2) = 101.5 degrees

therefore arc sin(x) = 101.5

apply sin to both sides

x = sin (101.5) ………………..again because sin (arc sin) = 1

from calculator again :

x=0.979 !!

cheers
moshe

##### Share on other sites
quote:
Original post by Fella
I know that But how do you solve this without a calculator?

Use maths tables , or Taylor series and lots of paper . I dunno. I don''t think it''s really possible without a calculator (or tables). Why don''t you want to use one?

Miles

##### Share on other sites
Remember that sin2 Θ + cos2 Θ = 1
From this, you can find that sin(arccos(x)) = sqrt(1 - x2)

And then, sqrt(1 - 0.22) = 0.979795897

/me adds a medal to his collection

[edited by - Beer Hunter on September 10, 2002 6:34:56 PM]

##### Share on other sites
quote:
Original post by Beer Hunter
Remember that sin2 ¦¨ + cos2 ¦¨ = 1
From this, you can find that sin(arccos(x)) = sqrt(1 - x2)

Could you write the intermediary steps? I'm missing something, here.

Oh, and be quick, this thread is going to be closed soon

Cédric

[edited by - cedricl on September 10, 2002 7:06:39 PM]

##### Share on other sites
quote:
Original post by Beer Hunter
Remember that sin2 È + cos2 È = 1
From this, you can find that sin(arccos(x)) = sqrt(1 - x2)

And then, sqrt(1 - 0.22) = 0.979795897

/me adds a medal to his collection

[edited by - Beer Hunter on September 10, 2002 6:34:56 PM]

Hey, that''s really cool! Never seen it before.

Miles

##### Share on other sites
You learn that in Algebra 2, Trig., or maybe even Geometry, if you have a good teacher.

Oh, and two things:

1) GAME ORIENTED QUESTIONS ONLY (or for the most part)
2) EVIDENCE OF PERSONAL EFFORT (no exceptions!)

1. 1
Rutin
44
2. 2
3. 3
4. 4
5. 5

• 10
• 28
• 20
• 9
• 20
• ### Forum Statistics

• Total Topics
633409
• Total Posts
3011703
• ### Who's Online (See full list)

There are no registered users currently online

×