Hello,

I am having trouble with this question, it say's:

Find all exact solutions in the interval [0,2[pi]).

a.) tan x= -2sin x

b.) sin^2 θ + 5cosθ +1=0

c.) sin^2 θ = -cos2θ

Any help would be greatly appreciated =)

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- Apr 29th 2010, 10:44 PMKAY03Finding exact solutions in the interval
Hello,

I am having trouble with this question, it say's:

Find all exact solutions in the interval [0,2[pi]).

a.) tan x= -2sin x

b.) sin^2 θ + 5cosθ +1=0

c.) sin^2 θ = -cos2θ

Any help would be greatly appreciated =) - Apr 29th 2010, 11:35 PMProve It
a)

or .

Case 1:

where .

Case 2:

where

where .

Putting it all together, we find

where .

In the interval , the solutions are:

where .

You may want to check these answers against the graph of though. Since I obtained the answers through squaring, it's possible that there are extraneous roots. - Apr 29th 2010, 11:46 PMProve It
- Apr 30th 2010, 12:05 AMProve It