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# Find all the values of x in the range 0° ≤ x ≤ 180° satisfying 4tan(x) + 7sin(x) = 0 watch

1. Hello everyone. I can't figure out how to solve the following:

Find all the values of x in the range 0° ≤ x ≤ 180° satisfying

4tan(x) + 7sin(x) = 0

Thanks for the help!
2. (Original post by Callanb)
Hello everyone. I can't figure out how to solve the following:

Find all the values of x in the range 0° ≤ x ≤ 180° satisfying

4tan(x) + 7sin(x) = 0

Thanks for the help!
You could write tanx = sins/cosx and factorize.
3. (Original post by RichE)
You could write tanx = sins/cosx and factorize.
thanks for the reply riche, i understood that i should use that identity but I am completely stuck on how to actually make anything useful of it.
4. (Original post by Callanb)
thanks for the reply riche, i understood that i should use that identity but I am completely stuck on how to actually make anything useful of it.
Like I said, factorize. Both expressions now have a sinx in them.
5. (Original post by Callanb)
thanks for the reply riche, i understood that i should use that identity but I am completely stuck on how to actually make anything useful of it.
u will have a sinx/cosx -7sinx.. then u can multiply it with cosx..

6. Solve further
7. (Original post by Mo3yman)

Solve further
You can't cancel all the sinx. You have to take the sinx out as it is common for both. So you get
Sinx(7cosX + 4)=0
SinX=0. CosX=-4/7
8. (Original post by Ackashh05012911)
You can't cancel all the sinx. You have to take the sinx out as it is common for both. So you get
Sinx(7cosX + 4)=0
SinX=0. CosX=-4/7
exactly
9. (Original post by Ackashh05012911)
You can't cancel all the sinx. You have to take the sinx out as it is common for both. So you get
Sinx(7cosX + 4)=0
SinX=0. CosX=-4/7
If there is ever one rule that I have learned:
Never cancel, just factor it out.
You more than likely lose a solution through division or cancellation if it isn't necessary.

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