Question

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?

Answer 1

@Shadow

Answer 2

I am here, are you ready?

Answer 3

Yes, sorry :P

Answer 4

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

Answer 5

That's okay if you don't know. Basically we start by visualizing the terminal side of angle theta.



It is in the second quadrant, and we have the point (-3,1)

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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.

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

I dont think so o.o

Answer 14

I think I do

Answer 15

Show me :)

Answer 16

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

Answer 17

Yes I need an example please XD

Answer 18

Let's say that our angle theta is at the circle I 'drew' so perfectly. Our sin (opposite over hypotenuse) would be:

\[\frac{ a }{ c }\]

Answer 19

OHHHH

Answer 20

:)

Answer 21

Do you think you got these now? :)

Answer 22

I think I do now :O

Answer 23

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

Answer 24

Yes please :D Hold on

Answer 25

for cos would it be b/c? just curious

Answer 26

for cos would it be b/c? just curious

Answer 27

Yes

Answer 28

Mwahaha I understood your code ^_^

Answer 29

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

Answer 30

For sin/cos/tan yes

Answer 31

I got it I got it :O WOOOO

Answer 32

Good job :)

Answer 33

All thanks to you! :D

Answer 34

Haha, glad I could help