Question

What are the sine, cosine, and tangent of 7 pi over 4 radians?

Answer 1

@whpalmer4 can you help?

Answer 2

Do you have your unit circle handy?

Answer 3

Yes!

Answer 4

This one?

Answer 5

sure, that will work. I see \(\large\frac{7\pi}{4}\) on there

Answer 6

Yep that's it. My options are:

sin Θ = negative square root 2 over 2; cos Θ = negative square root 2 over 2; tan Θ = 1

sin Θ = negative square root 2 over 2; cos Θ = square root 2 over 2; tan Θ = 1


sin Θ = square root 2 over 2; cos Θ = negative square root 2 over 2 tan Θ = -1

sin Θ = negative square root 2 over 2; cos Θ = square root 2 over 2; tan Θ = -1

Answer 7

okay, the sin of the angle is the y value of the (x,y) point on the unit circle, right? the cos of the angle is the x value of the (x,y) point on the unit circle. tan of the angle is the sin/cos

Answer 8

Do I have to first convert the 7 pi / 4 into x / y?

Answer 9

no, find the angle \(7\pi/4\) on the unit circle, next to a line going from the origin to the circle. read the (x,y) value where the line meets the circle

Answer 10

Okay...so it's square root 2 / 2, square root 2 / 2
?

Answer 11

no....time to put on your thinking cap, or eyeglasses or something....what are the numbers in the parentheses at the end of the line labeled \(7\pi/4\)?

Answer 12

That is what's inside the parenthesis, towards the bottom left hand side it shows inside the circle 7 pi/4 and at the end of the red line, (sqrt2/2, sqrt2/2)

Answer 13

Look at the red line.

Answer 14

Here's a better unit circle for viewing online:

http://www.embeddedmath.com/downloads/files/unitcircle/unitcircle-letter.pdf

Answer 15

Oh, I see, there's a minus sign on the second fraction; (sqrt2/2, -sqrt2/2)
Is this right?

Answer 16

yes. and it should be intuitively obvious to you as well, given that the sin is the y value and the cos is the x value that the sin of that angle must be negative, because you are below the x-axis

Answer 17

Sorry, this is my first assignment on unit circles;
so it's between B and D.
How do I divide the 2's for tan?

Answer 18

to divide by a fraction, invert the denominator fraction and multiply instead:

\[\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b}*\frac{d}{c} = \frac{ad}{bc}\]

Answer 19

in this particular case, it's even easier:

\[\frac{-\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} =- \frac{\cancel{\frac{\sqrt{2}}{2}}}{\cancel{\frac{\sqrt{2}}{2}}} =-1\]

Answer 20

Oh, okay I get it. Thanks for explaining:)

Answer 21

Ty sm!!! This was correct, just took the test!