high school pre cal- trigonometry HW

[finite sky]

Idk what I'm supposed to do

[balmy prawn]

do you know what the unit circle is?

[finite sky]

@balmy prawn yeah, i think

It's the circle with pie symbols all over it

[balmy prawn]

yeah

on the unit circle, the points (x, y) are the same as (cos(theta), sin(theta))

[finite sky]

What is theta

[balmy prawn]

the angle

so if you were asked for sin(pi/4)

you would look at the unit circle and see pi/4 is associated with the point (root2/2 , root2/2)

and the answer is the y-coordinate, since it's sin

[finite sky]

Cos would be the x-coordinate, right

Then what about tan, sec, and all the others?

[balmy prawn]

yep!

[balmy prawn]

tan is sin(theta)/cos(theta), so y/x

and then sec(theta) = 1/cos(theta) , csc(theta) = 1/sin(theta) , and cot(theta) = cos(theta)/sin(theta) = 1/tan(theta)

[finite sky]

For example, in question 3
Would the answer be
(square2)/2

[balmy prawn]

remember it's y/x for tangent

[finite sky]

So they would swap places?

[balmy prawn]

so it would be ((square2)/2)/((square2)/2)

which you can simplify to just 1

[finite sky]

So if sin = y
Cos = x
Tan would equal
Tan= sin/cos?

So what would r be for
Csc=r/y

[balmy prawn]

yes

[balmy prawn]

r on the unit circle is 1, so yes

$\csc{\theta}=\frac{1}{\sin{\theta}}$

[finite sky]

Oh

[analog hedge]

barometer

[finite sky]

That makes a lot more sense

[balmy prawn]

yeah

the unit circle is called the unit circle because the radius is 1 unit

[finite sky]

What about the quadrant, would that change my answers?

[balmy prawn]

it shouldn't

it's just dividing the hw into sections

[finite sky]

Oh

Thanks so much you made me understand it

[balmy prawn]

for instance, $\sin{\frac{3\pi}{4}}=\frac{-\sqrt{2}}{2}$

[analog hedge]

barometer

[balmy prawn]

good luck 🙏

[finite sky]

Thanks

[balmy prawn]

.close