How do i get rid of the zero factor ?

[Nemo's]

Homework Statement

lim (sinθ-1/2)/(θ-∏/6)
θ→∏/6

Homework Equations

The Attempt at a Solution

Direct substitution with ∏/6 gives 0/0
How do i get rid of the zero factor ?

 

[jedishrfu]

Direct substitution with ∏/6 gives 0/0
How do i get rid of the zero factor ?

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?

 

[ShayanJ]

You can use L'Hôpital's rule.

 

[Nemo's]

My textbook 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.

 

[jedishrfu]

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

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

 

[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 $\lim_{x\rightarrow 0} \frac{\sin{ax}}{bx}=\frac{a}{b}$

 

[jedishrfu]

Shyan great hint...

 

[ShayanJ]

Shyan great hint...

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

;)