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# C3 Trig watch

1. 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.
2. for a start -14.1 doesn't satisfy 0 < x < 360
3. 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!
5. are there any more values for alpha aside from 55? tan is positive when??

also too, right?

so could be 84

which works

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

=

square both sides and solve your quad in cosx. it's just plain nicer.
6. 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.
7. (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....
8. 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!
9. 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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