ThisGirlPretty:

The point (−3, 1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ?

7 months ago
ThisGirlPretty:

@Shadow

7 months ago
Shadow:

I am here, are you ready?

7 months ago
ThisGirlPretty:

Yes, sorry :P

7 months ago
Shadow:

Do you have an idea of how we would start solving this problem?

7 months ago
Shadow:

That's okay if you don't know. Basically we start by visualizing the terminal side of angle theta. |dw:1511200903857:dw| It is in the second quadrant, and we have the point (-3,1)

7 months ago
Shadow:

Essentially what we do, is draw a line from (-3, 1) to the x-axis, to create a triangle, as you can see here. https://www.desmos.com/calculator/zjgy3esqim

7 months ago
Shadow:

Then we define our sides, how long they are, then find sin, cos, and tan in terms of angle theta.

7 months ago
GucciAbe:

The coordinates of a circle with radius 1 are (cos(theta), sin(theta)) (-3, 1) designates a circle with radius radical 10, as 3^2+1=10, square root of 10 is radical 10 thus the coordinates are (2cos(theta). 2sin(theta)). -3=2cos(theta), -3/(10^0.5) is cos(theta) 1 is 2sin(theta), 1/(10^0.5) is sin(theta) tangent is sin(theta)/cos(theta), or -1/3

7 months ago
Shadow:

We know due to (-3,1) that our triangle is one unit high (1). It also stretches three units along the negative x-axis (-3). Now that we have two sides of our triangle defined, we can solve for the third side, our hypotenuse, using Pythagorean's Theorem. \[a^2 + b^2 = c^2\] \[(1)^2 + (-3)^2 = c^2\] \[c = \sqrt 10\] Now that we have our three sides, we can write sin, cos, and tan in terms of our angle theta.

7 months ago
Shadow:

|dw:1511201462789:dw| Our theta is at the origin. If you know SOH CAH TOA you can find them easy. Sin = opposite/hypotenuse Cos = adjacent/hypotenuse Tan = opposite/adjacent

7 months ago
ThisGirlPretty:

Okie, thank you and is there anything you want me to try? Btw how do you understand this type of language o.o

7 months ago
Shadow:

You know how to write for sin, cos, and tan, correct?

7 months ago
ThisGirlPretty:

I dont think so o.o

7 months ago
ThisGirlPretty:

I think I do

7 months ago
Shadow:

Show me :)

7 months ago
Shadow:

If you don't, that's ok. I can do an example

7 months ago
ThisGirlPretty:

Yes I need an example please XD

7 months ago
Shadow:

|dw:1511202085443:dw| Let's say that our angle theta is at the circle I 'drew' so perfectly. Our sin (opposite over hypotenuse) would be: \[\frac{ a }{ c }\]

7 months ago
Shadow:

|dw:1511202193827:dw|

7 months ago
ThisGirlPretty:

OHHHH

7 months ago
Shadow:

:)

7 months ago
Shadow:

|dw:1511202275542:dw| Do you think you got these now? :)

7 months ago
ThisGirlPretty:

I think I do now :O

7 months ago
Shadow:

Remember, our angle theta is at the origin (0,0). I can check your answers if you wish.

7 months ago
ThisGirlPretty:

Yes please :D Hold on

7 months ago
ThisGirlPretty:

for cos would it be b/c? just curious

7 months ago
ThisGirlPretty:

for cos would it be b/c? just curious

7 months ago
Shadow:

Yes

7 months ago
ThisGirlPretty:

Mwahaha I understood your code ^_^

7 months ago
ThisGirlPretty:

Would it be 1/sqrt 10 -3/sqrt 1/-3

7 months ago
Shadow:

For sin/cos/tan yes

7 months ago
ThisGirlPretty:

I got it I got it :O WOOOO

7 months ago
Shadow:

Good job :)

7 months ago
ThisGirlPretty:

All thanks to you! :D

7 months ago
Shadow:

Haha, glad I could help

7 months ago