C3 Trig

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.

Reply 1

Jelly_Beans_=]

for a start -14.1 doesn't satisfy 0 < x < 360

Reply 2

fait

OP

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!

post your workings?

OP

7sinx + 10cosx = rsin\theta*cos\alpha + rcos\theta*sin\alpha[br][br]rcos\alpha = 7[br][br]rsin\alpha = 10[br][br]r^2 = 10^2 + 7^2[br][br]r = \sqrt 149[br][br]tan\alpha = 10/7[br][br]\alpha = 55[br][br]\therefore \sqrt149sin (\theta + 55) = 8[br][br](\theta + 55) = 40.9[br][br]\theta = -14.1[br][br]\therefore \theta = 165.9[br][br][br][br][br][br][br][br]

Reply 5

Rocious

12

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.

Reply 6

fait

OP

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.

Reply 7

Rocious

12

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....

Reply 8

fait

OP

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!

Reply 9

fait

OP

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. :biggrin:

C3 Trig

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