Hello! I was wondering if any of you could help me with this problem:

Find the exact value of:

cos80^{o }- cos25^{o}

I have been taught to start off by adding or subtracting two degrees to get each of these, using a chart that gives all the Sine, Cosine, Tangent, Cotangent, Secant, and Cosecant values for the degrees (and matching radians) of:

0, 30, 45, 60, 90, 120, 135, 150, 180, 210, 225, 240, 270, 300, 315, 330, and 360 degrees.

However, I can't find any two numbers that will add up to or subtract to 80 or 25.

After I found that, I would use Sum and Difference Identities on cos80^{o} and cos25^{o} separately, and then subtract them at the end.

Am I going about this the right way? or is there another way to solve the problem?

Thank you very, very much!

Lily C

LilyC
Apr 17, 2017

#1**+3 **

I am sorry, I do not know how to find the exact value of cos80º - cos25º

But I am interested in this problem..if no one else knows how to do it, can you ask your teacher about it?

If there is a way to find the exact value of it I would be very interested to know it!!!

hectictar
Apr 18, 2017

#2**+3 **

I think heueka may know how to do this......WolframAlpha does not give a nice, neat "exact" value.....but......that doesn't mean that one doesn't exist.....!!!!!

CPhill
Apr 18, 2017

#3**+1 **

Thanks CPhill and Hectictar for trying this problem! I'll definitely ask her. She didn't review it completely when I asked before (I DID, however, realize that there's a different method when it comes to these), but we're going to have some time to review for our final in our next few classes, so I'll let you know how it goes!

Thanks again!

Lily

LilyC
Apr 26, 2017