The challenge trignometry question is: simplify sin⁡(80∘)+sin⁡(40∘) using trignometric identities. All the angle values are...

Shamar Padilla

Shamar Padilla

Answered

2022-01-26

The challenge trignometry question is: simplify sin(80)+sin(40) using trignometric identities. All the angle values are in degrees.
This is what I did: Let a=40. So we have sin(2a)+sin(a). Using the formula for sin(2a), I have,
2sin(a)cos(a)+sin(a)=sin(40)(2cos(40)+1)
All I got was a big red mark through the question. I looked at co-functions and half-angles and couldn't find a solution that came out to something I could do without a calculator. Any thoughts?

Answer & Explanation

lilwhitelieyc

lilwhitelieyc

Expert

2022-01-27Added 10 answers

You may have been intended to write
sin(80)+sin(40)=2sin(80+402)cos(80402)
=2sin(60)cos(20)
=3cos(20)
but I don't have a nice value for cos(20) and neither does Alpha, which finds about 0.93969. The first two terms of the Taylor series should be close, and if you know π210 you can write cos(20)112(π9)21101621116=0.9375 which is very close.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?