Problem with sum to product identities

J

Joanna

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Dec 1, 2011
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18
Cos(-pie/24) - cos(7pie/24)
I applied the sum to product identity and got:
-2sin [ (-pie/24 + 7pie/24) / 2] sin [ (-pie/24 - 7pie/24) /2]= - 2sin( pie/8) sin(-pie/6)
And I need the answer find the answer with out using the calculator and I know that pie/6= 30 degrees which means that sin of 30 degrees is (radical 3)/2 but the pie/8 equals 22.5 which is not a common angle... So I'm not sure if I made a mistake or if there is a different way of finding the answer so please help I have been stuck on this problem for 3 hrs now :/
 
1) "pie" is for eating. "pi" is for mathematics and for greek spelling.
2) 22.5º is a wondefully "common" angle, being exactly ½ of 45º.

Check your work and be sure. Remember all your other formulas, too!
 
​
so am I able to use the half angle identities to find sin(pi/8)
Sin(45/2)= + or - the square root of[ (1-cos45) /(2) ] Is that ok?
 
can someone let me know if what I mention in the last post was correct??
 
Joanna said:
so am I able to use the half angle identities to find sin(pi/8)
Sin(45/2)= + or - the square root of[ (1-cos45) /(2) ] Is that ok?
Click to expand...

Not quite. A little up-front consideration will help you see it more clearly. The general half-angle identity includes that nasty symbol "+/-", but you are working in the first quadrant. The sine is always positive in the first quadrant. Just use "+" at such times. Un-confuse yourself from the beginning. No need to wait for the end and wonder if you are on the right track. ;)
 
Subhotosh Khan said:
Did you mean \(\displaystyle \dfrac{\pi}{2}\)?
Click to expand...

DOH!

No, I meant to type 1/2 * Pi/4, not 2 * Pi/4, replying to the OP's question about whether the half-angle identity could be used to find sin(22.5 degrees).

I fixed the goof. Thanx. :oops:
 
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