Science:Math Exam Resources/Courses/MATH100/December 2016/Question 04 (b)
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Question 04 (b) 

Simplify . 
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! 
Hint 

Start from , and then find . 
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.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Let . So . Draw a simple triangle expressing this — opposite=4, adjacent = 1, so hypotenuse = ;
To be sure of the sign, note that the arctangent of a positive number lies between and and the sine of such a number is positive. Hence . 
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