How do you find the exact value of cos 7pi/4?

3 Answers
Apr 15, 2016

cos(5.49778714377)=0.70710678117.

Explanation:

Evaluate 7xxpi then divide that by 4 first
So 7xxpi is 7xxpi or 21.9911485751

7xxpi=21.9911485751

Now divide 7xxpi by 4

21.9911485751/4=5.49778714377

That means cos (7)(pi)/4 is cos(5.49778714377)

cos(5.49778714377)=0.70710678117.

Apr 16, 2016

First, convert to degrees (for many people, these are more convenient to work with).

Explanation:

The conversion factor between radians and degrees is 180/pi

(7pi)/4 xx 180/pi

=315^@

Now, this is a special angle, which can be found by using the special triangles.

But first, we must determine the reference angle of 315^@. The reference angle beta of any positive angle theta is within the interval 0^@ <= beta < 90^@, linking the terminal side of theta to the x axis. The closest intersection with the x axis for 315^@ would be at 360^@: 360^@ - 315^@ = 45^@. Our reference angle is 45^@.

We now know that we must use the 45-45-90; 1, 1 sqrt(2) triangle, as shown in the following graphic.

http://www.shmoop.com/trig-functions/special-trig-angle-obtuse.htmlhttp://www.shmoop.com/trig-functions/special-trig-angle-obtuse.html

Now, it's just a matter of applying the definition of cos to find the wanted trig ratio.

cos = adjacent/hypotenuse

cos = 1/sqrt(2), or 0.707, as a fellow contributor stated. However, for the purpose of this problem, I think your teacher would be looking for an exact value answer: cos((7pi)/4) = 1/sqrt(2)

Hopefully this helps!

Apr 16, 2016

sqrt2/2

Explanation:

Trig unit circle and trig table -->
cos ((7pi)/4) = cos (-pi/4 + (8pi)/4) = cos (-pi/4 + 2pi) =
cos (-pi/4) = cos (pi/4) = sqrt2/2