Trigonometric Equation
Medal!!

Question

Trigonometric Equation
Medal!!

anonymous · Answer

just a moment

anonymous · Answer

attachment

anonymous · Answer

@hartnn @amonoconnor @Directrix @jim_thompson5910 @perl @Loser66

hartnn · Answer

whats tan 45 ? 
and formula for tan(A+B) ? 
know any of these ?

anonymous · Answer

yup

hartnn · Answer

?

anonymous · Answer

1 and 
tan A+ tan B/1-tanAtanB

hartnn · Answer

yes,
so you getting any ideas out of it ? 

*hint* write 1 = tan 45

anonymous · Answer

nope.......I have to solve it with graphs!!

hartnn · Answer

wot? i would never use graph for this....and idk how to use it for this problem.....

anonymous · Answer

Pls can u write down the method??
I am kinda in a hurry today,pls....and have to turn this in tomorrow!!

hartnn · Answer

i can solve it algebraically

anonymous · Answer

okay.......:)

hartnn · Answer

LHS = (tan 45 + tan x) / (1- tan 45 tan x) = ... ?

anonymous · Answer

$$\tan((\pi/4)+x)\ge \tan(\pi/3)$$

hartnn · Answer

ok, 
solve tan (pi/4+x) = sqrt 3 
you'll get endpoints
can you graph tan (pi/4+x)
(so we'll need a graph for this, because of that >= sign)

anonymous · Answer

nope/..........no idea on such graphs

anonymous · Answer

can do tanx,cosx,sinx

hartnn · Answer

tan (x+pi/4) is just tan x shifted by pi/4 units on left

anonymous · Answer

o_O

anonymous · Answer

think I need way more than that.lol:)

hartnn · Answer

yes, 
f(x+a) is f(x) shifted by a units on left
f(x-a) is f(x) shifted by a units on right

hartnn · Answer

you can plot tan, right ?
just shift it by pi/4 units on left!

anonymous · Answer

I know.that....just dunno how the graph will look!!

anonymous · Answer

so tan(-pi/4) will coincide with origin??

hartnn · Answer

at origin, x =0 
so your graph will have the value tan (pi/4) =1

anonymous · Answer

ya

hartnn · Answer

graph y= tan (x+pi/4)
graph y= sqrt 3 (a line)
intersection points are your solutions for x

anonymous · Answer

whats the range ???

anonymous · Answer

can u pls draw it??  *.*

hartnn · Answer

hartnn · Answer

this plots both, line and tan graphs also shows you intersection points which are your solutions http://www.wolframalpha.com/input/?i=tan+%28x%2Bpi%2F4%29+%3D+sqrt+3

anonymous · Answer

Thank u...
Will post some more.Stay tuned!!

hartnn · Answer

welcome ^_^