Math Is Fun Forum

serena

Member

Registered: 2009-03-12

Posts: 13

trignometrical identities and simple equations Q1)

solve the following equations for θ, in the interval 0<θ≤ 360°

a) (sin θ - 1)(5cos θ +3) = 0
&
b) tan θ= tan θ(2+3 sin θ)

Last edited by serena (2009-03-12 22:52:23)

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,422

Re: trignometrical identities and simple equations Q1)

a) (sin θ - 1)(5cos θ +3) = 0
= 5sinθ cosθ  +3sinθ  - 5cosθ  - 3 = 0
= 5cosθ (sinθ -1) = 3(1-sinθ)
= 5cosθ = -3.
cosθ  = -3/5

b) tan θ= tan θ(2+3 sin θ)
Cancelling tanθ on the LHSand RHS,
1 = 2 + 3 sinθ
-1 = 3 sinθ
sinθ = -1/3

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serena

Member

Registered: 2009-03-12

Posts: 13

Re: trignometrical identities and simple equations Q1)

thnx a lot