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

Question

Use trigonometric function values of quadrantal angles to evaluate each expression.                                                                                                                                                                                                                            
                                                                                                                                                                                                                                                                                                                                                                                 
  3 sec 180° ― 5 tan 360°

Accepted Answer

Hey, everyone here, we are asked to determine the value of the given trigonometric expression. 16 multiplied by second of 360 degrees minus multiplied by tangent of degrees. Here we have four answer choice options, answer choice. A negative 11, answer B five, answer C 11 and answer D 16. So to begin determining the value of our given expression, we want to go term by term. So we can begin with 16 multiplied by sin of 360 degrees. And so our first step here is to recall the trigonometric identity, which states that sin is equivalent to one divided by cosine. So in our expression, we have second of 360 degrees. So utilizing our identity, we know that this expression is equivalent to one divided by cosine of 360 degrees. And now we just need to recall that cosine of degrees is just one. So simplifying we have one divided by one which just gives us one. So now substituting in this value into our expression, we have 16 multiplied by one minus 11 multiplied by tangent of 180 degrees. And now we just want to simplify. So 16 multiplied by one just gives us 16. So our expression so far is 16 minus 11 multiplied by tangent of 180 degrees. So now simplifying our second term, we need to recall the trigonometric identity where we know that tangent is equivalent to sine divided by cosine. So in our expression, we have tangent of 180 degrees. And once again, utilizing our trigonometric identity, we know that tangent is equivalent to sine of 180 degrees divided by cosine of 180 degrees. And now we just need to recall further that sign of 180 degrees is just zero and cosine of 180 degrees is negative one. So now simplifying our expression, we have zero divided by one and simplifying further, we just get zero. So now substituting in this value into our expression so far, we have 16 minus multiplied by zero. And now simplifying further, we are just left with 16. Therefore, we are left with answer choice D where again the value of our given expression is 16. 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. 3 sec 180° ― 5 tan 360°

Key Concepts

Quadrantal Angles

Trigonometric Functions

Evaluating Trigonometric Expressions

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