Question

Reduce each of the following to a function of a positive angle less than 45 degrees:
a. sin 175 degrees

Answer 1

@myininaya

Answer 2

so are you saying we want to convert to sin(x) such that x is between 0 and 45 degrees?

Answer 3

yep.. how dude :D

Answer 4

http://www.mathsisfun.com/geometry/images/circle-unit-304560.gif
Look at this unit circle...
What do you notice about sin(150) and sin(30)?

Answer 5

THE sign is different.

Answer 6

Look again..
sin(150)=sin(30)=1/2

Answer 7

oh.. yeah

Answer 8

Both sin(150)=sin(30) and sin(180-150)=sin(30)
... what about sin(135) and sin(45)
or sin(120) and sin(60)

Answer 9

So we have sin(150)=sin(180-150)=sin(30)
We also have sin(135)=sin(180-135)=sin(45)
And sin(120)=sin(180-120)=sin(60)
You should be able to use this pattern to make a guess what sin(175) equals

Answer 10

how?

Answer 11

All of those angles I just looked at or between 90 and 180...
175 is between 90 and 180

Answer 12

the pattern should still follow

Answer 13

Well I looked at angles from 90 to 180 and compared them to angles from 0 to 90

Answer 14

But each time what did we do?

Answer 15

You should a number that isn't changing in the process...

Answer 16

so cos 5 ?

Answer 17

sin(150)=sin(180-150)=sin(30)
sin(135)=sin(180-135)=sin(45)
sin(120)=sin(180-120)=sin(60)

Answer 18

or i will use sin 5 ?

Answer 19

Well is sin(150)=sin(30) or cos(30)?

Answer 20

Look at the unit circle.

Answer 21

sin 180 - 5

Answer 22

it is sin

Answer 23

sin( ?)

Answer 24

What is your final answer?

Answer 25

because i use 180 degrees? so its sin 5?

Answer 26

yes sin(5)

Answer 27

oh yeah i got it

Answer 28

but how about cot 321degrees 54 min.

Answer 29

so i will use sin360 - sin38.6 = -sin 38.6?