sin(2x+10@)=4sin(2x-10@)
2007-04-17 01:55:46 · 3 answers · asked by Boffin 2 in Science & Mathematics ➔ Mathematics
@ means degree
2007-04-17 02:18:57 · update #1
Does the @ symbol mean degrees here?
I will assume such.
So you have
sin 2x cos 10 + cos 2x sin 10 = 4( sin 2x cos 10 - cos 2x sin 10)
3 sin 2x cos 10 = 5cos 2x sin 10.
3 tan 2x = 5 tan 10.
Now use tan 2x = 2 tan x/ (1- tan²x)
tan x /(1-tan²x) = 5/3 tan 10 * (1/2) = 5/6 tan 10.
Let's set 5/6 tan 10 = t, just to make the typing easier.
Then tan x = t(1 - tan² x)
tan² x + tan x/t -1 = 0.
Now you have a quadratic which you can solve for
tan x. Then use your calculator to solve for x.
I'll let you carry on from here!
2007-04-17 02:26:59 · answer #1 · answered by steiner1745 7 · 0⤊ 0⤋
There is nothing actually wrong with the previous answer but it can be done more quickly. When you get to
3tan2x = 5tan10
tan2x = (5/3)tan10
2x = arctan((5/3)tan10)
x = (1/2)arctan((5/3)tan10)
and evaluate the right hand side with a calculator.
2007-04-17 09:34:09 · answer #2 · answered by mathsmanretired 7 · 0⤊ 0⤋
What is the @ symbol?
2007-04-17 09:09:09 · answer #3 · answered by Dave 6 · 0⤊ 0⤋