AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
QuestionGiven and that angle is in Quadrant IV, find the exact value of in simplest radical form using a rational denominator.Answer Attempt out of
Full solution
Q. QuestionGiven and that angle is in Quadrant IV, find the exact value of in simplest radical form using a rational denominator.Answer Attempt out of
- Recall Tangent Definition: Recall the definition of the tangent function in terms of sine and cosine: . Since is negative in Quadrant IV and cosine is positive in Quadrant IV, sine must be negative. We also know that , which is the Pythagorean identity.
- Representing sin and cos: Given , we can represent and as and , where is the hypotenuse of the right triangle formed by the angle . We need to find the value of using the Pythagorean identity.
- Finding Value of k: Using the Pythagorean identity , we substitute the values of and to find : , since is the hypotenuse and must be positive.
- Calculating csc A: Now that we have , we can find . The cosecant function is the reciprocal of the sine function, so .
- Calculating : Now that we have , we can find . The cosecant function is the reciprocal of the sine function, so .Calculate using the value of :Since we are looking for the exact value in simplest radical form with a rational denominator, we need to check if the sine value can be expressed in radical form. However, since is already in simplest form and does not involve a radical, this is the final answer.
