What is the largest angle for sin and tan to agree within 2 significant figures?

[homeworkboy]

For small angles theta, the numerical value of sin theta is approximately the same as the

numerical value of tan theta.Find the largest angle for which sine and tangent agree to within

two significant figures.

 

[homeworkboy]

anyone??

 

[swooshfactory]

I'm just learning this myself, but I would make a triangle, with an extremely long adjacent side and plug in values for theta (I think you'll have to find the opposite side for each angle). I'm not really too sure where that would lead, or if it's the right advice, but it's a place to start. Find an angle that is equal to just two (I think) significant figures and then add small increments to theta. Take this advice with a grain of salt though.

 

[grosenblatt]

hmm well basically its saying find the highest value of Ø such as sin(Ø) = tan(Ø) up to the second decimal place. I am guessing a lot of guessing/checking?

 

[LowlyPion]

For small angles theta, the numerical value of sin theta is approximately the same as the

numerical value of tan theta.Find the largest angle for which sine and tangent agree to within

two significant figures.

What do you know about the approximations that might lead you to be able to calculate it without guessing about it?

What is the approximation of

$$Sin\theta \approx \Delta x$$

$$Tan\theta \approx \Delta x$$

based on?

 

[homeworkboy]

im not sure what you mean

 

[homeworkboy]

i need to submit my assignment by 7 in the morning, so if you could be more clear. Thank You

 

[LowlyPion]

im not sure what you mean

$$Sin x \approx x$$

Similarly

$$Tan x \approx \ x$$

$$Tan x = \frac{Sin x}{Cos x} \approx \frac{x}{1 - x}$$

So what is the difference between the 2? That is what you want to identify where the divergence occurs.

 

[homeworkboy]

Im sorry i don't understand what you mean. I am only a freshman its my first assignment. I just don't get it. youve got to be more clear

 

[LowlyPion]

Im sorry i don't understand what you mean. I am only a freshman its my first assignment. I just don't get it. youve got to be more clear

This might explain it better than I can.

http://en.wikipedia.org/wiki/Small-angle_formula

I rewrote the previous equations all in x and maybe that will be less confusing.

 

[LowlyPion]

In particular this passage:

When one angle of a right triangle is small, its hypotenuse is approximately equal in length to the leg adjacent to the small angle, so the cosine is approximately 1. The short leg is approximately equal to the arc from the long leg to the hypotenuse, so the sine and tangent are both approximated by the value of the angle in radians.

 

[saikumar24]

how the letter(ex:a) will be converted into waves?

 

[saikumar24]

actually u r correct , but when we come to tan values and sin values in degree
they are same in some region ,so we will consider as same

 

[saikumar24]

yes you are correct but we will consider them as same values in rare cases and the consideration may nullify some errors.