Find exact values of the six trigonometric functions of each a...

Question

Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. 300°

Accepted Answer

List the six trigonometric function values of the following angle provide exact values when necessary to rationalize the denominator where we have the angle 315 degrees. And I've also placed a unit circle here with all of our angle measures. Now first, we can find 315 degrees. We noticed 315 degrees is in quadrant four. And we can go ahead and circle our point being the squared of two divided by two and negative squared of two divided by two. Now we can start finding our functions. We know the sign of data is equals to Y divided by R which is the hypotony of triangle R is given by the square root of X squared plus Y squared. We know R will then be the square root of the square of two divided by two squared plus negative square root of two divided by two squared. We get the square root of two divided by four plus two, divided by four, which gives us a spirit of one, which is just one, our assigned data then will then be the squared of two divided by two, which is negative divided by R which is one we see sine theta then is negative squares of two divided by two. Now we do the same for cosine cosine data. We should know is X divided by R which is our positive squared of two divided by two divided by one, we get squared of two divided by two for cosine. Now, you know a tangent, it's just our Y divided by our X or our sine data divided by our cosine data which gives us negative squares of two divided by two all divided by the square of two divided by two. We get negative one for our tangent. Now we can find our final three angles. We have our co K which is the reciprocal of sun. That is one divided by sun. That will be one divided by negative squares of two divided by two, which gives us two divided by the square of two which is negative. Now, we have to rationalize which if we multiply both the top and the bottom by the square of two divided by the square of two, we get negative squares to two as a code and data. Now you can also find our seeking data will be one divided by cosine data which is one divided by squared of two divided by two, which is just positive squared to two. Finally, we can find our cotangent data which is one divided by the tangent of data which we have one divided by negative one which is just one but negative. Again, we now have all six of our functions sine data of negative squares, two divided by two cosine data of the squared of two divided by two tangent negative one tangent nine of one, the negative squared of two and second theta positive squared of two. OK. I hope they help you solve the problem. Thank you for watching. Goodbye.

Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. 300°

Key Concepts

Unit Circle and Angle Measurement

Definition of the Six Trigonometric Functions

Rationalizing Denominators

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