Solving for all possible values of Ө

[bubbly16]

I'm having trouble starting these two problems. If possible would someone mind doing one of these as a step by step example?




b) 3tan(2Ө) – 3 = 0

I know that tan(2Ө)=1 but after this I'm lost on how to isolate Ө by itself.




c) sinӨ + 1 = cosӨ

I moved the one to the other side to create the equation sinӨ=cosӨ -1. From what I remember about this formula is that it has been proven "true" because both sides equal each other but should i divide by sin to get the side to 0?

 

[Deleted member 4993]

I'm having trouble starting these two problems. If possible would someone mind doing one of these as a step by step example?




b) 3tan(2Ө) – 3 = 0





c) sinӨ + 1 = cosӨ

3tan(2Θ) - 3 = 0

3tan(2\(\displaystyle \theta\)) = 3

Continue...

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[Explorer]

I'm having trouble starting these two problems. If possible would someone mind doing one of these as a step by step example?




b) 3tan(2Ө) – 3 = 0

I know that tan(2Ө)=1 but after this I'm lost on how to isolate Ө by itself.




c) sinӨ + 1 = cosӨ

I moved the one to the other side to create the equation sinӨ=cosӨ -1. From what I remember about this formula is that it has been proven "true" because both sides equal each other but should i divide by sin to get the side to 0?

For (b), after reducing the result to tan(2Ө) = 1, you can call 2Ө = x, and simply solve tanx = 1 (since you want all the solutions, remember to add kPI to the result).
After you have the solutions in x, get Ө = x/2.

For (c), solve
{
{ sinӨ + 1 = cosӨ
{ sinӨ^2 + cosӨ^2 = 1
{