Trig Identities Prob
'Solve sin x + 4 cos x = 3'
Can anyone help me with the above problem? Trigonometric identities and formulae confuse me.
I have tried doing this:
sin x = 3 - 4 cos x
divide all by cos x
then tan x = 3/cos x - 4
rearrange so 4 = 3/cos x - tan x
which is same as 4 = 3 sec x - tan x
square both sides
so 16 = 9 sec^2 x - tan^2 x
this is 16 = 9(tan^2x + 1) - tan^2 x
and 16 = 9tan^2x - tan^2x + 9
rearrange so 7 = 8 tan^2 x
7/8 = tan^2 x
so tan x= sqrt(7/8)
and x = arctan sqrt(7/8)
Is this correct?
If anyone could provide any help or solution to this problem, I'll be so grateful.
It's a lot easier with only one function.
why would you even know such an identity? :p
Originally Posted by TKHunny
so... is my answer right or wrong?
if wrong, what's right? lol
You started off well, but you squared incorrectly . . .
You should have: .
It's a philosophy, "Derive, Don't Memorize." (Wink)
Originally Posted by Jhevon