Question

what is the exact value of sin (3pi/4)?

Answer 1

It depends on what x is.

Answer 2

sorry i meant pi

Answer 3

\[\sin \frac{ 3\pi }{ 4 }\]

Answer 4

Ok, that's better.
Do you know what 3pi/4 is in degrees?

Answer 5

Sin(π-π/4)
What is sin(π-x)?

Answer 6

Or, do you know how to graph that angle in standard position with a unit circle?

Answer 7

i got 135 degree

Answer 8

Correct.
3pi/4 rad = 135 deg.

Answer 9

The figure above shows the 3pi/4 angle in standard position.
What is the angle the terminal side makes with the negative x-axis?
It's the angle marked alpha below.

Answer 10

45

Answer 11

Sin(π-x)=sinx if x is acute...
Here, sin(π-π/4)=sinπ/4

Answer 12

Yes, π/4 radians=45°

Answer 13

Correct.
That angle is the reference angle for a 135-deg angle.
The values of the sin, cos, tan, etc of an angle in standard position are the same as the values for the reference angle with the possible difference of a sign (positive or negative).

Answer 14

What is sin 45 deg?

Answer 15

0.7071 thanks man

Answer 16

You want the exact value, so it's \(\dfrac{\sqrt{2}}{2} \)

Answer 17

Since 135 deg and 45 deg both have terminal sides above the x-axis, they are both positive, so the answer in simply \(\dfrac{\sqrt{2}}{2} \) .

Answer 18

You're welcome.

Answer 19

how do u get that value?

Answer 20

This is one of those memorized values for sin, cos, tan.
Here is a way of doing it.