This is GREAT stuff. You do not want to be bad at it. Reread the section and make sure you get it. It will help you.
Can you answer the questions from there? If not, go back a couple of sections and read them over. You DO need this stuff.
Hi folks been really stuck on this question on my homework, any help what so ever would be extremely apprieciated.
Write 3sin(x)-4cos(x) in the form Asin(x+x*) * l.h.s sign is an x but the left sides on it are joined not sure what the signs called lol* and give the amplitude and phase. Hence find the general solution of 3sin(x)-4cos(x)=2.
Although the formula is correct, it might not give you the right answer when you enter this into your calculator; it is important to remember that this formula comes from the angle that a point (x=a, y=b) makes with the origin. This leads to the above formula and the equivalent formulas and and the quadrant is in is determined by the sine (+ or -) of a and b. The actual value of might be different from what your calculator tells you if is not in the quadrant your calculator is expecting it to be in. For example, if your a and b were negative your would be based on a point in the third quadrant and would therefore be between pi and 3pi/2 (in degrees, between 180 and 270). However, if you used the tangent formula and entered a negative a divided by a negative b the calculator would read this as a positive and number and give an answer in the 1s quadrant (between zero and pi/2, in degrees between 0 and 90). If you used the sin function your answer would be in the fourth quadrant, probably written as a negative value (between zero and -pi/2, in degrees between 0 and -90). Using the cos formula would give an answer in the 2nd quadrant (between pi/2 and pi, in degrees between 90 and 180). However, the actual value of is none of these. Therefore, the formula given in the previous would be more correctly written as where n=0 if a is positive and n=1 if a is negative. The cos formula would be better written as where n=0 if b is positive and n=2 if b is negative. The tan formula would be better written as where n=0 is a is positive and n=1 if a is negative.
Basically, when solving a problem like the one presented, chose one of the three formulas to find a value for using your calculator, and check to make sure this answer is in the same quadrant as (b,a). If it isn't, and you were using the tan formula, add pi (180 degrees) to your answer. If is in the wrong quadrant and you were using the cos formula, reflect your answer around the x axis, and if you get an answer in the wrong quadrant using the sin formula reflect your answer about the y axis.
LOL, at the time I found this post, I was trying to figure the answer to the question I answered on the post for a Differential equations take-home quiz. Even though the post didn't answer my question I figured it out by thinking about it and reviewing my notes, so I figured I'd be nice and putt a better answer for future frantic google searchers stuck in my position. Also that was my first post, and I also didn't realize how long it takes to takes to use that equation editor, but once I got started I couldn't let all my hard work go to waste.