anonymous
  • anonymous
Assuming cos t = .45 and cos w = .89, both t and w are positive, and both t and w determine a terminal point in quadrant 1, then which of the following statements best describes the relationship between t and w? A. t > w B. w > t C. It is not possible to tell from the given information.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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freckles
  • freckles
Have you looked at the first quadrant and notice what happens as the cos(t) values increase? like what happens to t?
freckles
  • freckles
you are given t and w are positive
freckles
  • freckles
so yes

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freckles
  • freckles
but that doesn't answer your question
freckles
  • freckles
https://www.mathsisfun.com/geometry/images/circle-unit-304560.gif Look at this picture what is cos(60) and cos(30) equal to?
anonymous
  • anonymous
cos(60) = 1/2 and cos(30) = \[\sqrt{3}/2\]
freckles
  • freckles
\[60^o >30^o \\ \cos(60^o)=\frac{1}{2} ? \frac{\sqrt{3}}{2}=\cos(30^o)\] which of those values are greater ?
freckles
  • freckles
is 1 bigger than sqrt(3) or is sqrt(3) bigger than 1?
anonymous
  • anonymous
sqrt(3) is bigger than 1
freckles
  • freckles
\[60^o>30^o \\ \cos(60^o)<\cos(30^o) \\ \text{ and you have } \cos(t)<\cos(w)\] and since we know t and w are in the first quadrant just like 60deg and 30deg was then we know what about t and w?
anonymous
  • anonymous
We know that t < w?
freckles
  • freckles
why? didn't we have that cos(60)30 ?
anonymous
  • anonymous
Was it because of the cosine?
freckles
  • freckles
what does that mean?
anonymous
  • anonymous
The cosine of 60 is giving us a value that is less than our cosine of 30 I think
freckles
  • freckles
yes 1/2 is less than sqrt(3)/2
anonymous
  • anonymous
So the answer would be w > t (B)?
freckles
  • freckles
ok see if you follow this: \[60^o>30^o \\ \text{ so } \cos(60^o)=\frac{1}{2}<\frac{\sqrt{3}}{2}=\cos(30^o) \\ \text{ we have} \cos(60^o)<\cos(30^o) \text{ but } 60^o>30^o \\ \text{ You are given } \cos(t)<\cos(w) \text{ so you can draw what conclusion about } t?w\] hint replace 60 with t and 30 with w
freckles
  • freckles
you can also notice in the first quadrant as the angle increases the cos value of those angles decrease
anonymous
  • anonymous
So if the equations decreased that would make t > w?
anonymous
  • anonymous
Great! Thank you!!!
freckles
  • freckles
yes

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