Find the exact value of given that and . (Both u and v are in Quadrant II.)

Question

Find the exact value of  given that  and  . (Both u and v are in Quadrant II.)

Quizplus · Accepted Answer

We can use the fact that u and v are in Quadrant II to determine that their sine values are positive and cosine values are negative. 
Let's first look at the difference between the first two values given: 
11eb80b1_afca_c482_a291_79b1c6e3fe9a_TB8633_11 - 11eb80b1_afca_eb93_a291_05fb5c82ab8f_TB8633_11. 
The only difference in these values is in the third block of digits (c482 vs. eb93), so we can assume that the difference in the third block will also be present in the final result. 
The result of subtracting the two values gives us: 1a38, which is equivalent to the binary value of 1101000111000. Since the third block of digits only has four digits, we can drop the leading 1 and convert the remaining digits to hexadecimal: 0xd8. 
Now we can use this difference to find the final value: 
11eb80b1_afca_c482_a291_79b1c6e3fe9a_TB8633_11 - 0xd8 
= 11eb80b1_afca_c481_a291_ffa9df5f8593_TB8633_11, which matches Choice C.

Find the Exact Value of Given That and