Without using a calculator, decide whether each function value...

Question

Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that π ≈ 3.14.)

tan 6.29

Accepted Answer

Welcome back. I am so glad you're here. We're asked to determine whether the value of the trigonometric function is positive or negative do not use a calculator. Our trigonometric function is the tangent of 7.2. How our answer choices are answer choice, a positive and answer choice B negative. All right. So we've got this angle of 7.2 radiance. So the first question is which quadrant is 7.2 radiance in. So let's draw a rough sketch of a cordate plane. We've got a vertical Y axis, a horizontal X axis. They come together the origin in the middle. The first quadrant is up into the right of the origin. The second quadrant is up into the left of the origin. The third quadrant is down into the left of the origin and the fourth quadrant is down into the right of the origin. So where is 7.2? Well, we recall from previous lessons that one full rotation around our circle would be two pi radians. That would be right back to the positive part of the X axis. Half of that, that would be the negative part of the X axis is pi radiance half of that. So that's the positive part of the Y axis because we're heading counterclockwise half of pi is pi divided by two and three quarters of a rotation around. This is the negative part of the Y axis would be three pi divided by two radiance. And now you could use a calculator to figure out what those are in numbers. But if we take pi divided by two, that's approximately 1.57 pi is approximately 3.14 three. Pi divided by two is approximately 4.71 and two. Pi is approximately 6.28. So where is 7.2? Well, 7.2 is actually bigger than 6.28. So what we want to do is find a co terminal angle for 7.2 that is in between zero and two pie. Now it's also important to keep in mind that two pi is also zero. OK. So to find a co terminal angle will take 7.2 and subtract one full rotation which is two pi 7.2 minus two, pi is approximately 0.920 0.92 is in between zero and 1.57. So we are in the first quadrant. So now the question becomes, is tangent positive or negative in the first quadrant. Well, we recall from previous lessons that all of our trigonometric functions are positive in the first quadrant. So the tangent of 7.2 that's positive. In the first quadrant, we look at our answer choices and that matches with answer choice. A well done. We'll catch you on the next one.

Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that π ≈ 3.14.)

tan 6.29

Key Concepts

Quadrantal Angles

Unit Circle

Tangent Function

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