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lofti

Guest

Trigonometric equations

so, I'm having a little trouble with a few problems on trig.
can someone help me please.

solve each equation for 0<= x <= 2 pie

1.) square root of 2 tan x = 2 sin x

2.) cot squared x - csc x = 1

3.) find all values of theta between 0 and 2pie that satisfy -1 - 3 sin theta = cos 2 theta

Solve each equation for all real values of x

1.) 2 cos squared x = 3 sin x

2.) cos squared x - sin squared x = square root of 3/2

3.) 2 sin x + csc x = 3

solve each inequality for 0 <= theta <= 2pie

1.) cos theta - 1/2 > 0

2.) sin 2x < sin x for 0 <= x <= 2pie

on the interval 0 degrees  <= x < 360 degrees how many solutions are expected for the equation
a sin(bx + c) + d = d + a/2 if a is not equal to 0 and b is any positive interger

once again thanks for the help

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: Trigonometric equations

okay, the trick with these is to basically get all the trig functions on one side, and all the numbers on the other.

1.

so

so

this you have to solve just by familiarity. The solution in this case happens to be 45 degrees or pi/4.

I don't have time right now to do all of them, but they're really quite easy. All you really need to know is the following identities:

the Pythagorean identities:

and

whenever you see a squared trig funciton, like sin^2 x or cos^2 x and a 1 present, its a dead giveaway, you have to use one of the Pythagorean identities.

hope this helps.

Last edited by mikau (2007-11-26 10:48:01)

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