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

Question

Use trigonometric function values of quadrantal angles to evaluate each expression.                                                                                                                                                                                                                            
                                                                                                                                                                                                                                                                                                                                                                                 
  ―3(sin 90°)⁴  + 4(cos 180°)³

Accepted Answer

Welcome back. I am so glad you're here. We are asked to determine the value of the given trigonometric expression. Our given trigonometric expression is negative 13 multiplied by the sign of 270 degrees. Raced to the fourth power plus 18, multiplied by the cosine of 270 degrees cubed. Our answer choices are answer choice. A negative 13 answer choice B 18, answer choice C five and answer choice D 13. All right. So we notice that our angles here are both degrees and 270 degrees is a quadrant angle. And there are exact values for the trigonometric functions of quadrant angles. We recall from the tables in our book and previous lessons that the sign of 270 degrees is equal to the exact value of negative one. So for the first term here, we've got negative 13 multiplied by negative one raised to the fourth power. And then that's plus and for this other one, the cosine of 270 degrees also has an exact value that exact value is zero. So if 18 multiplied by zero, cute. And so now it's just a matter of simplifying this starting with exponents, negative one raised to the fourth power is positive one. So you have negative 13 multiplied by positive one plus 18, multiplied by zero. Cubed is still zero. Now the multiplication step negative 13 multiplied by one is negative 13 and then 18 multiplied by zero is zero and negative 13 plus zero is negative 13. So the value of our trigonometric function is negative 13. We look at our answer choices and this matches with answer choice. A 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. ―3(sin 90°)⁴ + 4(cos 180°)³