## anonymous one year ago 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.

1. freckles

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

2. freckles

you are given t and w are positive

3. freckles

so yes

4. freckles

5. freckles

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

6. anonymous

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

7. freckles

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

8. freckles

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

9. anonymous

sqrt(3) is bigger than 1

10. 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?

11. anonymous

We know that t < w?

12. freckles

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

13. anonymous

Was it because of the cosine?

14. freckles

what does that mean?

15. anonymous

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

16. freckles

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

17. anonymous

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

18. 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

19. freckles

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

20. anonymous

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

21. anonymous

Great! Thank you!!!

22. freckles

yes