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.

Question

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.

freckles · Answer

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

freckles · Answer

you are given t and w are positive

freckles · Answer

so yes

freckles · Answer

but that doesn't answer your question

freckles · Answer

https://www.mathsisfun.com/geometry/images/circle-unit-304560.gif Look at this picture what is cos(60) and cos(30) equal to?

anonymous · Answer

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

freckles · Answer

$$60^o >30^o \ \cos(60^o)=\frac{1}{2} ? \frac{\sqrt{3}}{2}=\cos(30^o)$$
which of those values are greater ?

freckles · Answer

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

anonymous · Answer

sqrt(3) is bigger than 1

freckles · Answer

$$60^o>30^o \ \cos(60^o)<\cos(30^o) \ \text{ and you have } \cos(t)<\cos(w)$$
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 · Answer

We know that t < w?

freckles · Answer

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

anonymous · Answer

Was it because of the cosine?

freckles · Answer

what does that mean?

anonymous · Answer

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

freckles · Answer

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

anonymous · Answer

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

freckles · Answer

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 · Answer

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

anonymous · Answer

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

anonymous · Answer

Great! Thank you!!!

freckles · Answer

yes