Use trigonometric function values of quadrantal angles to evaluat...

Question

Use trigonometric function values of quadrantal angles to evaluate each expression.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               [cos(―180°)]²  + [sin(― 180°)]²

Accepted Answer

Welcome back. I am so glad you're here. We're asked to determine the value of the given trigonometric expression. Our given expression is the cosine of negative 270 degrees squared plus the sign of negative 90 degrees squared. Our answer choices are answer choice. A one answer, choice B two answer choice C zero and answer choice D negative one. All right. So we'll take a look at our expression and we notice that these angles, we have a negative 270 degrees and a negative 90 degrees. Those are both quadrant angles. And there are exact values for the trigonometric functions of quadrant angles. So we can get some exact values here. First, let's get our angles in between zero and 360 degree. So first, we can start with this negative 270 degrees to get that between zero and 360 degrees. We'll add one full rotation. So we'll add 360 degrees and that comes out to a positive 90 degrees. So this is a co terminal angle with the cosine of 90 degrees that will be squaring. And so we'll be able to get an exact value for that. And now let's take a look at the sign of negative 90 degrees. We'll take the negative 90 degrees. And again, we'll add 360 degrees, add one full rotation. And we will get with that 1, 270 degrees. So we are adding the sign of a co terminal angle with our negative 90 degrees which is 270 degrees and then we'll square that. So we recall from previous lessons and from the tables in the book that the cosine of 90 degrees is equal to zero. So we've got zero squared for the exact value for the first one. And from those same tables and previous lessons, the sign of 270 degrees is negative one. So we'll be squaring negative one. Well, zero squared is zero plus negative one squared is a positive one and zero plus one is positive one. And so the value of our given trigonometric expression is one. We look at our answer choices and that matches with answer choice. A well done. We'll catch you on the next one.

Use trigonometric function values of quadrantal angles to evaluate each expression. [cos(―180°)]² + [sin(― 180°)]²

Key Concepts

Quadrantal Angles

Trigonometric Function Values

Pythagorean Identity

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