Concept Check Work each problem.What angle does the line y = √3x ...

Question

Concept Check Work each problem.What angle does the line y = √3x make with the positive x-axis?

Accepted Answer

Welcome back. Everyone in this problem, we want to identify the acute angle formed between the line defined by Y equals the squared of three divided by three multiplied by X and the Y axis. For our answer choices, A is 30 degrees, B is 45 degrees C is 60 degrees and D is 75 degrees. Now, what do we know here? Well, we, we, we are trying to figure out the angle formed between a line and the Y axis, the acute angle formed. That is, so let's try to make sense of what's really going on. So we have our X and Y axes and we're talking about a line. So I'll put that in red, whose equation is Y equals the square root of three divided by three X. OK. And notice that for our line, we want the acute angle. So we're talking about the A, the acute angle between the line and the x axis. No, given that it's a line, we know that it's a general form. Recall that the general form of a line equals MX plus B where M is the slope and B is the intercept. Also recall that if theta is an acute angle formed by a line passing through the origin and the positive X axis, then its slope, the slope of the line equals the tangent of theta or the tangent of our angle. So M equals the tangent of theta. So what does that tell us? Then that tells us that if we can figure out what our slope is, the value of M, then we can substitute it to figure out our acute angle formed between the line and the X axis. But we don't know what M is M is our slope. It's the coefficient of X. And notice that the coefficient of X is the square of three divided by three. So since M or slope equals the square of three divided by three, then that tells us that the tangent of theta equals the square of three divided by three. No, we'll be able to solve for theta because that means theta would be equal to the inverse tangent of the square of three divided by three. And when we put that value into our calculator, then we find that theta equals degrees which when we look back in our answer choices would have been answer choice. A thanks a lot for watching everyone. I hope this video helped.

Concept Check Work each problem.What angle does the line y = √3x make with the positive x-axis?

Key Concepts

Slope of a Line

Tangent of an Angle

Inverse Tangent Function

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