Question 07 (b)
Find all values of satisfying the equation in the interval . Justify your answer.
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 hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
Solving the equation will be similar to the previous question - you'll want to know the values of and at certain angles. However the answer will be different from before - how is this equation different than the previous equation?
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
This question is similar to the previous one, except we are using the derivative:
Setting this equal to zero and moving a term over gives
This means that and must have equal values but opposite signs. On the unit circle, corresponds to x-values and corresponds to y-values, so the opposite signs place us in quadrant II of the coordinate plane (the restriction of rules out quadrant IV). The angle where the values of and are equal in this quadrant is , so .