lgg23
  • lgg23
Suppose sin (t) = (x/5) and the angle t is in the first quadrant. Write algebraic expression for cos (t) and tan (t) in terms of x.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Draw a triangle with a side x and a hypotenuse 5. Then let the angle opposite of side x be angle t. We imagine the angle t growing from 0 to pi/2 while keeping the hypotenuse at 5 units. As we do this, that the side of length x grows too. So the ratio x/5 changes. Anyways, in this triangle, the remaining side is found using the Pythagorean theorem. It is sqrt(25 - x^2). So then we see that for any t between 0 and pi/2, cos t = sqrt(25 - x^2)/5. And also tan t = x/sqrt(25 - x^2).. These are the expressions in terms of x you're looking for.
lgg23
  • lgg23
Thank you.

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