SOLUTION: 7. If tan(x) = 2 and x ∈ [180◦ , 270◦ ]. Determine the value of (i) cos(x) (ii) sin(x) (iii) the angle x

Algebra ->  Trigonometry-basics -> SOLUTION: 7. If tan(x) = 2 and x ∈ [180◦ , 270◦ ]. Determine the value of (i) cos(x) (ii) sin(x) (iii) the angle x      Log On


   

Question 1077232: 7. If tan(x) = 2 and x ∈ [180◦ , 270◦ ]. Determine the value of
(i) cos(x)
(ii) sin(x)
(iii) the angle x
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

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tan%28x%29+=+2 —> +x=tan%5E-1%282%29+=+63.4349%5Eo+ and since +tan%28x%29+=+b%2Fa+: +a=-1+, b=-2
But since we're in Q3, we need to add 180%5Eo to get it into standard form (where the angle is measured from the +x axis counterclockwise).
(iii) +highlight%28x=243.4349%5Eo%29+ in standard form.
+h+=+sqrt%28a%5E2+%2B+b%5E2%29+=+sqrt%28%28-1%29%5E2%2B%28-2%29%5E2%29+=+sqrt%285%29+
(i) +cos%28x%29+=+a%2Fh+=+highlight%28-1%2Fsqrt%285%29%29+ or approx. -0.447214
(ii) +sin%28x%29+=+b%2Fh+=+highlight%28-2%2Fsqrt%285%29%29+ or approx. -0.894427
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NOTE: Just be aware: often you will want to normalize things so you have a unit circle (i.e. r=1). I did not use a unit circle (h=sqrt(5)). To do that I would have had to divide a,b, and h by sqrt(5). However, since the problem only dealt with ratios of the sides, the lack of normalization didn't matter.