Question

Find the exact values of cos(3pi/4 radians)
and sin(3pi/4 radians?

Answer 1

i am so comfused does anyone know how to solve this? @golden_bullets @phi @Destinymasha i don't get the exact value thing.

Answer 2

@mathmale

Answer 3

You want (first):\[\cos \frac{ 3\pi }{ 4 }.\]

Answer 4

The "unit circle" has four Quadrants. Do you know in which Quadrant you'll find 3Pi/4 radians? Hint: Pi radians = 180 degrees.

Answer 5

Hint: 3Pi/4 radians = 135 degrees. In which quadrant will you find this angle?

Answer 6

i think i understand. so um to convert it it would be 3/4 of 180 right which is 135
so on the unit circle 135 is \[-\sqrt{2}/2,\sqrt{2/2}\]

Answer 7

The angle 3Pi/4 = 135 degrees is in the 2nd Quadrant and looks like this:

Answer 8

(cos, sin) so that is how you find the exact value. am i right?

Answer 9

The cosine of 3Pi/4 is\[\cos \frac{ 3\pi }{ 4 }=\frac{ adj~side }{ hypotenuse }=\frac{ -1 }{ \sqrt{2} }\]

Answer 10

this is exactly the same as your\[\frac{ -\sqrt{2} }{ 2 }.\] The sine of this angle is the same as the cosine, EXCEPT that it is positive. Your second result should be discarded in favor of -Sqrt(2)/2.

Answer 11

these are the "exact" answers.

Answer 12

@mathmale can u finish helping me please? if u done helping her

Answer 13

what about the unit circle? I get what you just said but i don't understand why you need -1/\[\sqrt{2}\] did you use cos function instead of the unit circle and then do something to it.

Answer 14

As I understand this problem, we are to find (1) the cosine of 3Pi/4 and (2) the sine of 3Pi/4. You and I must know the definitions of both the sine and the cosine.
opp adj
sin x = --------- cos x = -----------
hyp hyp

Looking at the picture I drew for you, can you verify that the hyp is Sqrt(2), the adj side is -1 and the opp side is 1?

That's where the -1 comes from.

Do let me know if you have further questions about this!