Expert: Sherman D. - 1/15/2005

Question
complete each statement with one of the symbols <, >, or =.

1) cos.40°__ cos.30°
2) sin.310°__ sin.230°
3) cos.50° __ cos.(-50°)

i just want to know how to figure it out without using a calculator or table.  

Answer
1.)
cos(40°)__cos(30°)
.766 __ .866
ANS : <
Think about this, there are 360° in a circle. The closer you are to 0° or 360° the higher the value.
Since 30° is closer to 0°, cos(30°) is higher.

2.)
sin(310°)__sin(230°)
-.766__-.766
ANS : =

310° is at the same distance from 360° as 230° is from 180°, which is that they are both 50° from being at 0°, in otherwords, add 50° to 310°, you get 360°, which is 0° and if you subtract 50° from 230°, you get 180°. Also 310° is the same as -50° and 230° is the same as -50° when you flip the angle from right to left.

3.)
cos(50°)__cos(-50°)
.64278__.64278
ANS : =
50° is 50° above 0° and -50° is 50° below 360°, so since they are both the same distance from the 0° or 360° mark, and therefore they have the same answer.

I forgot the best way to explain this, since i haven't done angles in like 7 or 8 years.