# How do i get rid of the zero factor ?

1. Dec 6, 2013

### Nemo's

1. The problem statement, all variables and given/known data

lim (sinθ-1/2)/(θ-∏/6)
θ→∏/6

2. Relevant equations

3. The attempt at a solution
Direct substitution with ∏/6 gives 0/0
How do i get rid of the zero factor ?

2. Dec 6, 2013

### Staff: Mentor

You can't that why they want you to find the limit at that point.

You must use other means what does your textbook say about finding limits?

3. Dec 6, 2013

### ShayanJ

You can use L'Hôpital's rule.

4. Dec 6, 2013

### Nemo's

My text book explained using limθ→0 sinθ/θ =1, using trigonometric identites and multiplying by the conjugate (in case of algebraic expressions) to solve limits.
This question was in the differentiation section but it's before L'Hopital Rule so I guess there must be some other way.

5. Dec 6, 2013

### Staff: Mentor

You could transform it to something similar using phi = theta - pi/6 to get

lim phi->0 sin(phi + pi/6) / phi

6. Dec 6, 2013

### ShayanJ

Maybe the identity $\sin{\alpha}-\sin{\beta}=2 \sin{\frac{\alpha-\beta}{2}} \cos{\frac{\alpha+\beta}{2}}$ helps.
Also have in mind the more general formula $\lim_{x\rightarrow 0} \frac{\sin{ax}}{bx}=\frac{a}{b}$

Last edited: Dec 6, 2013
7. Dec 6, 2013

### Staff: Mentor

Shyan great hint...

Last edited: Dec 6, 2013
8. Dec 6, 2013

### ShayanJ

you...and more...Nemo's are welcome!!!

;)