Thread: Angle between line and x-axis.

The first problem that I can't wrap my head around is:

"Find the acute angle that is formed by the line y - sqrt(3x) + 1 = 0 and the x-axis."

The second problem is a very confusing word problem:

"Express the lengths a and b in the figure in terms of the trigonometric ratios of the angle."

Textbook's diagram recreated in Paint: http://i.imgur.com/FEwzP.png


Thank you!!

Originally Posted by neowoot

The first problem that I can't wrap my head around is:

"Find the acute angle that is formed by the line y - sqrt(3x) + 1 = 0 and the x-axis."
this is not an equation of a line

The second problem is a very confusing word problem:

"Express the lengths a and b in the figure in terms of the trigonometric ratios of the angle."
cos theta = a/b. i am not sure what length is marked as "1"
Textbook's diagram recreated in Paint: http://i.imgur.com/FEwzP.png


Thank you!!

......

Sorry! That is how the diagram is in the book. I am assuming that the length 1 is the same as the length of a.

As for the first problem, I have double-checked and I have written the problem verbatim... I don't know what is wrong.

Originally Posted by abhishekkgp

......

It is a line, just not a straight one. So the question makes sense, just not in trig.

CB

Originally Posted by CaptainBlack

It is a line, just not a straight one. So the question makes sense, just not in trig.

CB

even curves can be called lines?? now i am going to brag about it among my friends!they don't know this either.

Originally Posted by abhishekkgp

even curves can be called lines?? now i am going to brag about it among my friends!they don't know this either.

That is why "straight lines" require the qualifier "straight"

CB

Originally Posted by CaptainBlack

It is a line, just not a straight one. So the question makes sense, just not in trig.

CB

I disagree.

- A segment is the shortest distance between two points.

- A ray is also defined by a segment between two points, but then extended in one direction to be infinitely long.

- A line is defined by a segment between two points, but then extended to be infinitely long in both directions.

- A curve is defined by a sum of infinitessimally small line segments.

I expect that this question is asking for the magnitude of the acute angle formed by the TANGENT to the curve at the intercept, and the axis.

That's getting way off the point!

neowoot, I suspect that the equation you are given is really y - sqrt(3)x + 1 = 0. I have changed the parentheses so that x is no longer inside the square root. it is now (square root of 3) times x. You probably have learned that if y= mx+ b, then m is the "slope" of the line and is equal to the tangent of the angle the line makes with the x axis. What angle has tangent equal to sqrt(3)?

If the problem really is y- sqrt(3x)+ 1= 0, then you will need to find the derivative of y= sqrt(3x)- 1 to find the slope of the tangent line at x= 1/3. Is this a Calculus course?

As for (b), assuming that a= 1 would make 1/b= cos(theta) so that b= 1/cos(theta)= sec(theta). But since the problem asks you to find a in terms of the angle, "a= 1" seems strange.

I suspect that the "1" should be inside the circle indicating that the circle has radius 1. In that case, we have a right triangle with angle, with one leg of length "a", the other of length 1, and the hypotenuse of length "b". The angle where the hypotnuse and the leg of length "a" meet is theta.

Then tan(theta)= 1/a so a= cot(theta). And sin(theta)= 1/b so b= csc(theta).