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.)

cos 6

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. And our trigonometric function is the cosine of 5.1. Our answer choices are answer choice, a positive or answer choice B negative. All right. So we can look at this 5.1 and we see that that's a radiant measure. And what we can do is recall from previous lessons, the coordinate plane, we've got a vertical Y axis and a horizontal X axis. They come together the origin in the middle quadrant one is up to the right of the origin quadrant two is up into the left of the origin quadrant three is down into the left of the origin and quadrant four is down into the right of the origin. And uh 5.1 the angle 5.1 we want to figure out where that is which quadrant it's in. So we recall from previous lessons that one full rotation. So if our initial side is the positive part of the X axis, and we've got one full rotation around back to where we started that is two pi radiance half of that. So the negative part of the X axis half of two pi is pi half of that half of pi. So just one quarter of the way around a full rotation. And that's the positive part of the Y axis is pi divided by two and three quarters of a rotation. So that's the negative part of the Y axis is going to be three pi divided by two. If you plug those into a calculator, you can get an idea of an approximate number for each of those pi is about 3.14 half of that pi divided by two is about 1.57 two. Pi double, our 3.14 is about 6.28. And if we multiply our 3.14 by three halves, so three quarters of the rotation is about 4.71. And so our 5.1 is going to be in between 4.71 and 6.28. We are in the fourth quadrant. Now the question is, is cosine positive or negative in the fourth quadrant. So we recall from previous lessons for this one, we know the acronym. All students take calculus that tells us in the first quadrant. A, all of our trigonometric functions are positive in the first quadrant students. S tells us that the sine function is positive in the second quadrant along with its reciprocal function kant. In the third quadrant, all students take tt tells us that tangent is positive in the third quadrant along with its reciprocal function cotangent. And in the fourth quadrant, all students take calculus C tells us that cosine and its reciprocal function C can't are positive in the fourth quadrant. So there we have it cosine is positive in the fourth quadrant. So looking at our answer choices 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.)

cos 6

Key Concepts

Quadrantal Angles

Unit Circle

Radian Measure

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