anonymous
  • anonymous
Without using a calculator determine the exact value of sin(x - y) given that sin x = -1/3) , tan y = (1/3) , x is a quadrant II angle and y is a quadrant III angle.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
sin(x) shouldn't be negative if x is in the second quadrant. Is there a typo?
anonymous
  • anonymous
Im sorry the problem is Without using a calculator determine the exact value of cos(x - y) given that sin x = (1/3) , tan y = (1/3) , x is a quadrant II angle and y is a quadrant III angle.
anonymous
  • anonymous
its easy

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anonymous
  • anonymous
use sum/diff of angle expansion
anonymous
  • anonymous
= cos(x)cos(y)+sin(x)sin(y)
anonymous
  • anonymous
if sin(x) = (1/3) , draw up a general right angle triangle , mark an angle x ( obviously not the right angle ) , and label the opposite 1 and hypotenuse 3
anonymous
  • anonymous
then you can find the adjacent side by pythagorus , which works out as sqrt(8) therefore cos(x) = - sqrt(8) / 3 ( because x is negative in the 2nd quadrant
anonymous
  • anonymous
now you just need to find siny and cosy
anonymous
  • anonymous
Possible answers are \[A. 0 B. (12\sqrt{5} - \sqrt{10}) /30 C. (-12\sqrt{5} - \sqrt{10}) /30 D. (-12\sqrt{5} + \sqrt{10}) /30\] \[E. (12\sqrt{5} + \sqrt{10}) /30\]
anonymous
  • anonymous
with tan(y)=(1/3) , draw up a general right angle triangle , mark opposite as 1 and adjacent as 3
anonymous
  • anonymous
therefore the hypotenuse is sqrt(10) so sin(y) = - 1 / sqrt(10) and cosy =- 3/sqrt(10)
anonymous
  • anonymous
then sub in
anonymous
  • anonymous
So my equation should look like (-sqrt(8)/3 * -3/sqrt(10) ) + (1/3 * -1/sqrt(10)) ???

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