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

Question

Use trigonometric function values of quadrantal angles to evaluate each expression.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               tan 360° + 4 sin 180° + 5(cos 180°)²

Accepted Answer

Hey, everyone here, we are asked to determine the value of the given trigonometric expression where we have three multiplied by tangent of 180 degrees plus eight, multiplied by sine of 360 degrees plus 13, multiplied by the quantity of cosine of 360 degrees squared. Here we have four answer choice options, answer choice A eight answer B three answer C 13 and answer D 11. So to determine the value of our given expression, we can begin by simplifying each of the tangent sine and cosine terms. So we can begin with our first term here where we have tangent of 180 degrees. And to simplify this term, we just need to recall that tangent is equivalent to sine divided by cosine. And so here again, we have tangent of 180 degrees. So we now know that this is equivalent to sine of 180 degrees divided by cosine of 180 degrees. And next, we need to simplify our current expression utilizing our unit circle. So we can recall that sign of 180 degrees is equivalent to zero and cosine of 180 degrees is equivalent to negative one. And so here we now have zero divided by negative one. So simplifying our final simplified value for a tangent of 180 degrees is just zero. Now, we can move on to our next term in the given expression where we have sign of 360 degrees. And now once again, recalling our unit circle, we know that this term is equivalent to just zero. Now, lastly, we are given cosine of 360 degrees. Once again from the unit circle, we know that this term cosine of 360 degrees is equivalent to positive one. And so now that we have found each of the values for each of the tangent sine and cosine terms, we can now substitute in these values into our given expression. And so we have three multiplied by zero plus eight, multiplied by zero plus 13 multiplied by the quantity of one squared. So now simplifying our first two terms are just zero. So we have just zero plus zero. Next, we need to recall that one squared is just one. So we also have plus 13 multiplied by one. And now simplifying we have 13 multiplied by one which is just 13. Therefore, our final simplified value from the given expression leaves us with answer choice C where we have the value of 13. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Use trigonometric function values of quadrantal angles to evaluate each expression. tan 360° + 4 sin 180° + 5(cos 180°)²

Key Concepts

Quadrantal Angles

Trigonometric Function Values

Evaluating Expressions

Watch next