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    Solve the equation: 7sinx + 10cosx = 8 with 0 < x < 360.

    I solved the question using the rcos (a+b) approach but I got a wrong answer and I checked my working. I was just wondering when tackling these types of questions, what form is most appropriate? I used rsin(theta + alpha) so that's why I think I got the question wrong.

    Btw i got theta + 55 = 40.9

    Then, I got theta to be 165.9.
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    for a start -14.1 doesn't satisfy 0 < x < 360
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    I know, just posting that I got that to be the principal value to see if people get to the same spot. Guess i shoulda made it clearer!
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    post your workings?
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     7sinx + 10cosx = rsin\theta*cos\alpha + rcos\theta*sin\alpha



rcos\alpha = 7



rsin\alpha = 10



r^2 = 10^2 + 7^2



r = \sqrt 149



tan\alpha = 10/7



\alpha = 55



\therefore \sqrt149sin (\theta + 55) = 8



(\theta + 55) = 40.9



\theta = -14.1



\therefore \theta = 165.9
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    are there any more values for alpha aside from 55? tan is positive when??

    also \text{sin}(139.1) = \frac{8}{\sqrt{149}} too, right?

    so \theta could be 84

    which works

    \theta being 165.9 doesnt work. why do you think that is?

    also i HATE that method so much. it's so saucy.

    i would say 7\text{sin}x = 8 - 10\text{cos}x

    7\sqrt{1 - \text{cos}^2x} = 8 - 10\text{cos}x

    square both sides and solve your quad in cosx. it's just plain nicer.
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    tan is positive between 180 and 270, so alpha = 180 + 55, 235.

    Where did you get sin 139 from?

    Yeah, I get why theta being 165.9 doesnt work, because it would give a negative answer, wrong quadrant.
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    (Original post by fait)
    tan is positive between 180 and 270, so alpha = 180 + 55, 235.

    Where did you get sin 139 from?

    Yeah, I get why theta being 165.9 doesnt work, because it would give a negative answer, wrong quadrant.
    what is the value of arcsin 8/root149?

    sin is positive between 90 and 180....
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    Ah ****. I kept doing arctan.

    So arcsin 8/root149 = 40.9
    Other value: 139.1. Then you do -55, which gets you 84.1. Cheers!
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    Oh btw, the other solution I did works because you have to add 360 to the -14.1 which you get 345.9, another solution. And interesting method, I quite like it. Cheers again.
 
 
 
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Updated: November 9, 2008
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