Trig Identities

[JonathanEngr]

Hi, all. It's been YEARS since I've done trig identities, and although I remember many of them, half and double-angle formulas escape me. I'm a professional engineer by trade, so naturally my daughter asks for my help. I'm lost on this one, however. One of her homework problems is to prove the identity in the attached image. Any suggestions would be much appreciated to scrape the rust off of my brain!!

 

[Deleted member 4993]

Hi, all. It's been YEARS since I've done trig identities, and although I remember many of them, half and double-angle formulas escape me. I'm a professional engineer by trade, so naturally my daughter asks for my help. I'm lost on this one, however. One of her homework problems is to prove the identity in the attached image. Any suggestions would be much appreciated to scrape the rust off of my brain!! View attachment 25032

If I were to solve this problem I would start from Right-Hand-Side.

\(\displaystyle \frac{1+ sec(t)}{2*sec(t)} \ \)

\(\displaystyle = \frac{cos(t)+ 1}{2} \ \)

Now use cos(2x) = 2*cos²(x) - 1 and continue....

 

[Dr.Peterson]

Hi, all. It's been YEARS since I've done trig identities, and although I remember many of them, half and double-angle formulas escape me. I'm a professional engineer by trade, so naturally my daughter asks for my help. I'm lost on this one, however. One of her homework problems is to prove the identity in the attached image. Any suggestions would be much appreciated to scrape the rust off of my brain!! View attachment 25032

One good rust-removal tool is Google. I'd start, if I were you, by searching for a list of identities, or specifically for the half-angle identity.

But actually, even before that, I'd look in your daughter's book to see what identities are available to her, because that's what she needs to use. (I'd also ask to see her work, just as we do on this site!)

If she can use the half-angle identity, then you're halfway there. Multiply the numerator and denominator of the RHS by cos(theta) and see if that looks familiar.

If she hasn't learned that identity, try using the double angle identity.

 

[JonathanEngr]

Thanks, everyone! I eventually solved it with the "Google rust removal tool." The algebraic portion isn't the problem, but finding the correct identities was tough. I remember there being a somewhat finite list of identities when I was in college, or at least they confined specific identities to different chapters (half-angle, double-angle, etc.). Going through Google just showed an endless array of them. Oh--and trying to search google for things like "how to solve for sin theta/2 when you have the solution for tangent theta" is a bit cumbersome.

As for her book, well, let's just say that other things must have been on her mind when she was packing her bag at the end of the day Thanks again!

 

[Dr.Peterson]

I remember there being a somewhat finite list of identities when I was in college, or at least they confined specific identities to different chapters (half-angle, double-angle, etc.).

A single page like these is generally good enough:

• https://www.freemathhelp.com/trig-identities.html
• http://www.sosmath.com/trig/Trig5/trig5/trig5.html
• https://www.purplemath.com/modules/idents.htm

But, yes, choosing the right one at the right time is that part that takes skill, not just memory. Just make sure your daughter gets to develop the skill.