Expert: Paul Klarreich - 7/20/2006

Question

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Followup To

Question -
Sin theta10/2=5/12
Theta10=2*Sin-1(5/12)
Don't know what the next steps are to solve.


Answer -
Hi, Debora,
 
Question:  Sin theta10/2=5/12
Theta10=2*Sin-1(5/12)
Don't know what the next steps are to solve.
......................................
I'm not sure what your equation actually says.  Is it:

sin(t/2) = 5/12,   or is it:

sin t    5
----- = ---
 2     12

(writing 't' for 'theta')
My guess is that it is the first, since that seems more 'fun'.  But I don't understand what that '10' is doing there.  

Solving

sin(t/2) = 5/12, you are right to continue with:

t/2 = arcsin(5/12)

t = 2 arcsin(5/12)

Now there is not much left to do except compute 5/12 and find the arcsin (which you do on the calculator with the INV key and the SIN key.)

HOWEVER, I think you are headed for a problem like this:

Compute  sin(arctan(5/12))

which is much more interesting.  When you get to this problem, let me know.

when I solve this problem this is the answer I get and its not the right answer.Don't know what I am doing wrong? Must be using the calculator wrong. Could you break it down in a few more steps

t=2*sin-1(5/12)= 49.2486...
The answer is t=.8596 rad  

Answer
Hi, Debora,

>> Yes, that's the answer I get, too, actually the calculator says:

0.85955086260905537174785394946639

Did you remember to set the calculator to compute angles in radian measure?
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Subject:  Trigonometry
Private:  no
Question:  
-------------------------

Followup To

Question -
Sin theta10/2=5/12
Theta10=2*Sin-1(5/12)
Don't know what the next steps are to solve.


Answer -
Hi, Debora,

Question:  Sin theta10/2=5/12
Theta10=2*Sin-1(5/12)
Don't know what the next steps are to solve.
......................................
I'm not sure what your equation actually says.  Is it:

sin(t/2) = 5/12,   or is it:

sin t    5
----- = ---
2     12

(writing 't' for 'theta')
My guess is that it is the first, since that seems more 'fun'.  But I don't understand what that '10' is doing there.  

Solving

sin(t/2) = 5/12, you are right to continue with:

t/2 = arcsin(5/12)

t = 2 arcsin(5/12)

Now there is not much left to do except compute 5/12 and find the arcsin (which you do on the calculator with the INV key and the SIN key.)

HOWEVER, I think you are headed for a problem like this:

Compute  sin(arctan(5/12))

which is much more interesting.  When you get to this problem, let me know.

when I solve this problem this is the answer I get and its not the right answer.Don't know what I am doing wrong? Must be using the calculator wrong. Could you break it down in a few more steps

t=2*sin-1(5/12)= 49.2486...
The answer is t=.8596 rad