find the exact value of: cos315degrees?

Question

step by step?

Answer 1

315 is in the 4th quadrant, so
cos 315
= cos (360 - 315)
= cos 45
= (sqrt 2) / 2

Answer 2

It's 1/sqrt(2) or [sqrt(2)] / 2. Why?:

Measuring angles in degrees,

cos x = cos (360 + x), and also,

cos z = cos (- z).

Applying both of these relationships, we find that

cos 315 = cos (- 45) = cos (+ 45).

By Pythagoras's Theorem, a (45, 45, 90 deg.) triangle has sides of length 1, 1, and sqrt(2), so that cos 45 (= sin 45 also) = 1/sqrt(2) or [sqrt(2)] / 2.

Live long and prosper.

P.S. Since sqrt(2) is irrational, the value of 1/sqrt(2) for
cos (315 deg.) is as exact as one can write it. [Its numerical value is of course 0.707106781..., which while not exact is probably fine for all practical purposes!]

Answer 3

Find the exact value of: cos315degrees =cos 45 degrees
=sqrt(2)/2=0.7071 answer

Answer 4

cos 315 falls in QIV (fourth quadrant) , so we know the cosine will be positive.
315 +45 = 360 (therefore reference angle is 45)
cos 315 = cos 45
cos 45 = 1/sqrt2 OR rationalize (sqrt2) / 2 (many ways to find this) easiest is the right triangle and use SOHCAHTOA, cosine is adjacent / hypotenuse ... triangle legs are each 1 and hyp is sqrt2

Answer 5

It doesn't have an exact value; the value is 0.5 sqrt(2), which is irrational. The cosine of 0-45 degrees is equal to the cosine of 0+45 degrees.

Answer 6

cos 315° is in 4th quadrant so is + ve
cos 315° = cos 45° = 1 / √2

Answer 7

cos 315 = cos (360 -45) = cos360cos45 +sin360sin45=1*cos45 +0= cos45 =(sqrt2)/2

Answer 8

cos 315= 0.71

Answer 9

0.70710678118654752440084436210485

exactly