what is the exact value of cos of 285 degrees?

Question

please help and show work so i can understand it please!!!

Answer 1

- cos 15°
- cos (60 - 45)°
- [cos 60° cos 45° + sin 60° sin 45° ]
- [ (1/2)(1/√2) + (√3/2)(1/√2) ]
- [ (1 / (2√2) + (√3 / (2√2) ]
- (1 / (2√2) ) [ (1 + √3 ]

Answer 2

When you draw the angle 285 it is in the 4th quadrant. Since it is not in the first quadrant, you will need to find the reference angle. reference angle= l angle you have-the angle of closest x-axis l. This way your reference angle is always positive.
285 is in quad. 4.
l 285-360 l=75 degrees. You will need to find cos 75= cos(45+30), the formula for that is cosAcosB - sinAsinB
cos45cos30 - sin45sin30=
(square root2/2 * square root3/2) - (square root2/2 * 1/2)=
square root6/4 - square root2/4, or
(root6-root2)/4 is the cos285=cos75
(root6 - root2)/4 IS THE EXACT VALUE OF COS285. You can change it in decimal if you please.
Decimal value of that is .2588
Starry Eyed has that it would be cos(45-30) that would be cos15=.9659. That is wrong. They do have the correct formula though.
cos75=cos285=.2588

Answer 3

Here's a rational expression (exact) of cos(285) (in degrees)

cos (285) = cos(360 - 285)
= cos(75)
= cos(30+45)
= cos(30)cos(45) - sin(30)sin(45)
Now
cos(45) = sin(45) = 1/sqrt(2)
so
cos(285) = ( cos(30) - sin(30) ) / sqrt(2)
and
cos(30) = sqrt(3)/2
sin(30) = 1/2
giving
cos(285) = (sqrt(3) - 1)/(2 sqrt(2))
= (sqrt(3) - 1)sqrt(2)/4
an exact value !!!
Approximately
~ (1.732 - 1)(1.414)/4
= (0.732)(0.35354)
= 0.2588

Answer 4

Okay well I left my calculator in school, so i won't be able to give you the answer. I can tell you how to get it though....Take your calc. and enter in 'cos' (depending on your calculator you may have to hit a button before it, such as 2nd). Once you've got that just put in 285 and close your parentheses. So there you have, cosine of 285..it'll probably be a decimal so you'll have to round it. Oh, that's how i do it on my TI-89 titanium. Calcs vary though.

Answer 5

cos(285) = ((sqrt(3)-1)*sqrt(2))/4 from my TI-89. 285 degrees = 19pi/12 radians.

Answer 6

How exact do you want it?

Just by plugging into the calculator, you get
0.25881904510252076234889883762405

cos(285) = cos(-75) = cos(-60 - 15)
= cos(-60)cos(15) + sin(-60)sin(15)
= 0.5cos(45-30) + -sqrt(3)/2*sin(45 - 30)
= 0.5(cos(45)cos(30) + sin(45)sin(30)) - sqrt(3)/2 * (sin(45)cos(30) - cos(45)sin(30))
= 0.5(sqrt(2)/2 * sqrt(3)/2 + sqrt(2)/2 * 1/2) - sqrt(3)/2 * (sqrt(2)/2*sqrt(3)/2 - sqrt(2)/2*1/2)
= 0.5*(sqrt(6)/4 + sqrt(2)/4) - sqrt(3)/2*(sqrt(6)/4 - sqrt(2)/4)
= 0.5*(0.61237 + 0.35355) - 0.86603*(0.61237 - 0.35355)
= 0.5*(0.96593) - 0.86603*(0.25882)
= 0.48296 - 0.22414
= 0.25882

I used the identities

cos(u+v) = cos(u)cos(v) - sin(u)sin(v)
and
sin(u+v) = sin(u)cos(v) + cos(u)sin(v)

Answer 7

cos(285) = cos (3.pi/2-15)= cos(15) = cos(45-30)=
cos45.cos30 - sin45.sin30.

Answer 8

0.25881904510252

I think thats right.