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?

10 months ago
ThisGirlPretty:

10 months ago

I am here, are you ready?

10 months ago
ThisGirlPretty:

Yes, sorry :P

10 months ago

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

10 months ago

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)

10 months ago

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

10 months ago

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

10 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

10 months ago

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.

10 months ago

|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

10 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

10 months ago

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

10 months ago
ThisGirlPretty:

I dont think so o.o

10 months ago
ThisGirlPretty:

I think I do

10 months ago

Show me :)

10 months ago

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

10 months ago
ThisGirlPretty:

Yes I need an example please XD

10 months ago

|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: $\frac{ a }{ c }$

10 months ago

|dw:1511202193827:dw|

10 months ago
ThisGirlPretty:

OHHHH

10 months ago

:)

10 months ago

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

10 months ago
ThisGirlPretty:

I think I do now :O

10 months ago

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

10 months ago
ThisGirlPretty:

10 months ago
ThisGirlPretty:

for cos would it be b/c? just curious

10 months ago
ThisGirlPretty:

for cos would it be b/c? just curious

10 months ago

Yes

10 months ago
ThisGirlPretty:

Mwahaha I understood your code ^_^

10 months ago
ThisGirlPretty:

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

10 months ago

For sin/cos/tan yes

10 months ago
ThisGirlPretty:

I got it I got it :O WOOOO

10 months ago

Good job :)

10 months ago
ThisGirlPretty:

All thanks to you! :D

10 months ago