reduct this problem..

1/2 sinθ + http://upload.wikimedia.org/math/b/f...0c7e41b924.png/2 cos Θ

to the form

a. r sin (Θ+Φ)

b. r cos(Θ+Φ)

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- September 21st 2009, 08:10 AMjasonlewizreduction of a cosΘ+/_ b sinΘ
reduct this problem..

1/2 sinθ + http://upload.wikimedia.org/math/b/f...0c7e41b924.png/2 cos Θ

to the form

a. r sin (Θ+Φ)

b. r cos(Θ+Φ) - September 21st 2009, 08:15 AMskeeter
- September 21st 2009, 10:50 AMGrandadHandling expressions of the form a sin x + b cos x
Hello jasonlewizskeeter's solution is all you need for this particular problem. But, in case you don't spot that can be written as and that is the sine of the same angle ( ), here's the more general method for handling this type of expression:

Compare coefficients of and :

(1)

(2)

Divide (2) by (1):

Square (1) and (2) and add:

(taking the positive root)

So there are the values of and .

You can do part (b) in exactly the same way, but starting with . (In fact, it's slightly easier to start with since then turns out to be a positive angle.)

Grandad