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

3 Answers

cos(5.49778714377)=0.70710678117.

Explanation:

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

7×π=21.9911485751

Now divide 7×π by 4

21.99114857514=5.49778714377

That means cos(7)π4 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 180π

7π4×180π

=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 β of any positive angle θ is within the interval 0β<90, linking the terminal side of θ to the x axis. The closest intersection with the x axis for 315 would be at 360: 360315=45. Our reference angle is 45.

We now know that we must use the 454590;1,12 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=12, 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(7π4)=12

Hopefully this helps!

Apr 16, 2016

22

Explanation:

Trig unit circle and trig table -->
cos(7π4)=cos(π4+8π4)=cos(π4+2π)=
cos(π4)=cos(π4)=22