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GregA
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one of the questions is as follows:
7cosx +6sinx =2...the answer is required between 0 and 360 degrees.
I first tried to tackle it using rsin(x+y) giving rsiny = 7, rcosy = 6...
r = sqrt(85), y =49.4deg
sqrt85sin(x + 49.4deg) = 2...sin(x + 49.4deg) =2/sqrt85...
x + 49.4deg =+/- 12.53deg
this gives rise to 323.deg and 298.1deg...of which only 323.1deg is correct, the other answer is 118.1deg but I got this by checking the answers, scratching my head for a while and then using rcos(x-y) with just the positive square root of 85.
the book doesn't state which expression should be used and a different book implies that all of the 4 expressions will yield the same result in all situations...my question is how should I know which expression to use or is there something wrong with my working? (I do know with hindsight that the above question requires the cosine of x to be positive if the sine is negative and vice-versa)
(I also have noticed that the wrong answer I got is a rotation about 180deg of the correct answer...but I am sure that this is not the way I should be arriving at a solution)
7cosx +6sinx =2...the answer is required between 0 and 360 degrees.
I first tried to tackle it using rsin(x+y) giving rsiny = 7, rcosy = 6...
r = sqrt(85), y =49.4deg
sqrt85sin(x + 49.4deg) = 2...sin(x + 49.4deg) =2/sqrt85...
x + 49.4deg =+/- 12.53deg
this gives rise to 323.deg and 298.1deg...of which only 323.1deg is correct, the other answer is 118.1deg but I got this by checking the answers, scratching my head for a while and then using rcos(x-y) with just the positive square root of 85.
the book doesn't state which expression should be used and a different book implies that all of the 4 expressions will yield the same result in all situations...my question is how should I know which expression to use or is there something wrong with my working? (I do know with hindsight that the above question requires the cosine of x to be positive if the sine is negative and vice-versa)
(I also have noticed that the wrong answer I got is a rotation about 180deg of the correct answer...but I am sure that this is not the way I should be arriving at a solution)
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hit me like a hammer driving back home...and could only get back to the computer now