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.

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- anonymous

- schrodinger

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- freckles

Have you looked at the first quadrant and notice what happens as the cos(t) values increase? like what happens to t?

- freckles

you are given t and w are positive

- freckles

so yes

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## More answers

- freckles

but that doesn't answer your question

- 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

cos(60) = 1/2 and cos(30) = \[\sqrt{3}/2\]

- 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

is 1 bigger than sqrt(3) or is sqrt(3) bigger than 1?

- anonymous

sqrt(3) is bigger than 1

- 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

We know that t < w?

- freckles

why?
didn't we have that
cos(60)30 ?

- anonymous

Was it because of the cosine?

- freckles

what does that mean?

- anonymous

The cosine of 60 is giving us a value that is less than our cosine of 30 I think

- freckles

yes 1/2 is less than sqrt(3)/2

- anonymous

So the answer would be w > t (B)?

- 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

you can also notice in the first quadrant as the angle increases the cos value of those angles decrease

- anonymous

So if the equations decreased that would make t > w?

- anonymous

Great! Thank you!!!

- freckles

yes

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