math problem - trig help please?

Question

i need to find the radian measure of four angles in standard position that are coterminal with the given angle in standard position.

1. and i am given ∏(pi) / 4 pi over four

2. 7 ∏ / 5 seven pi over five

3. - ∏ / 6 negative pi over six

now i have the answer to the first one but i want to know how to do it the first one is

9 ∏ / 4 ; 17 ∏ / 4 ; - 7 ∏ / 4 ; - 15 ∏ / 4

but i also would like to better know what coterminal is so if someone could explain it i woud really like it.


thanks

Answer 1

Angles A and B are coterminal means that if you take a figure and rotate it by A radians, and then you take that same figure and instead rotate it by B radians, it will end up in the same place as when you rotated it by A radians. As an example, 0 and 2π are coterminal because if you rotate something through one full circle it will end up right back where it started. It follows that two angles are coterminal if and only if they differ by an integer multiple of 2π radians. So for #2, you would list answers of the form 7π/5 ± 2πk, where k is some integer. Examples would be 17π/5, 27π/5, 37π/5, 47π/5, -3π/5, -13π/5, -23π/5, -33π/5, and so forth. Similarly, for -π/6, you could have 11π/6, 23π/6, -13π/6, -25π/6, and the like.

Answer 2

First, Coterminal Angles mean:

"Angles which, drawn in standard position, share a terminal side. For example, 60°, -300°, and 780° are all coterminal."
(see: http://www.mathwords.com/c/coterminal.htm )

just add or subtract multiples of 2TT (2 pi) to get coterminal angles...

for (2), angle = 7 TT / 5

hence 7 TT/5 + 2TT = 17 TT / 5 is a coterminal angle
so is 7TT/5 - 2TT = - 3TT/5
and so on

Answer 3

do this sin120/cos45= tan(4x+ninety). then take the inverse tangent. could supply you tan^-a million(sin120/cos45) = 4x+ninety. you have got an entire quantity for the left ingredient then do exactly trouble-free algebra and subtract ninety from the left ingredient and then divide by using 4 and you have got your answer.