Math Is Fun Forum

RachelSmith

Guest

HELP.. identities and equations

Hey there!

I would appreciate it so much if someone could help me with these! I need the method and the answer, because the way I'm doing it seems to be all wrong.. I am not even sure I know what I'm doing.. So I need someone to explain it to me.. THANK YOU so much!

Use identities to obtain approximate solutions to these equations giving all answers to the nearest degree:

1) 3cos^2 x - sin x - 2 = 0, 0 _< x _< 360 degrees

2) 2cos^2x + 3 sin x = 3, 0 _< x _< 180 degrees

thank you so much!

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: HELP.. identities and equations

The identity you want here is cos² θ + sin² θ = 1.

Using this, you can convert the cos² x's into sin² x's. Then you've got a nice, easy quadratic equation which will let you find sin x. Then just take the inverse of that to find x.

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Why did the vector cross the road?
It wanted to be normal.

amonjezi

Member

Registered: 2006-03-09

Posts: 9

Re: HELP.. identities and equations

3cos^2x+3sinx=3 
3(1-sin^2x)-sinx-2=0
3-3sin^2x-sinx-2=0
3sin^2x+sinx-1=0
if sinx=y
3y^2+y-1=0
this equaition very easy (0 degree to 360 degree)

amonjezi

Member

Registered: 2006-03-09

Posts: 9

Re: HELP.. identities and equations

thank you rashel
your question is very good
by