Science:Math Exam Resources/Courses/MATH100/December 2014/Question 01 (e)
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Question 01 (e) 

If then is 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

How is defined? Try rearranging the equation and using implicit differentiation. 
Hint 2 

Use a trigonometric identity and give your final answer in terms of . 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Another way to write is . Taking the derivative with respect to on both sides gives To be able to solve for we use the trigonometric identity with . Solving for we find Since and cosine is positive in this interval we take the positive branch. Thus
Finally, solving for we find Hence, the final answer is C. 