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

Question

Use trigonometric function values of quadrantal angles to evaluate each expression.                                                                                                                                                                                                                            
                                                                                                                                                                                                                                                                                                                                                                                 
  (sec 180°)²  ―  3 (sin 360°)²  + cos 180°

Accepted Answer

Welcome back. I am so glad you're here. We're asked to determine the value of the given trigonometric expression. Our expression is the sea can't of 360 degrees squared minus 12 multiplied by the sign of 180 degrees squared plus the cosine of 90 degrees. Our answer choices are answer choice, a zero answer, choice B one answer, choice, C negative one and answer choice D negative 12. All right, we notice here with our expression that we have with our, all of our angles 360 degrees, 180 degrees and 90 degrees. All three of them are quadrant angles and there are exact values for the trigonometric functions of quadrant angles. So recalling from previous lessons and from the tables in the textbook for the C can of the quadrant angle 360 degrees, that's equal to one. So we can say instead of the C can of 360 degrees squared, we have one squared. And then for the sign of 180 degrees, the exact value of that is zero. So that one squared is then minus 12 multiplied not by the sign of 180 degrees. But by zero squared and then plus the cosine of 90 degrees looking at those tables, the exact value of that is zero. So now it's just a matter of simplifying one squared is one and then minus 12 multiplied by zero squared. Well, zero squared is zero, then plus zero, negative 12 multiplied by zero is zero. So I mean, we have one minus zero plus zero. That's just one. So the value of our given trigonometric expression is a positive one. We look at our answer choices and that matches with answer choice. B well done. We'll catch you on the next one.

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Use trigonometric function values of quadrantal angles to evaluate each expression. (sec 180°)² ― 3 (sin 360°)² + cos 180°