Question

Use the given triangles to evaluate the expression. Rationalize all denominators.
cos Pi/6

Answer 1

Hang on, what is the expression?

Answer 2

it is in the very first attchment

Answer 3

that is all it has

Answer 4

@johnweldon1993 oh its cos pi/6

Answer 5

@Garadon_Shagan

Answer 6

Ah okay lol, yeah I was like...are you sure?

regardless...Alright what does

\(\Large \frac{\pi}{6}\) equate to in degrees?

Answer 7

i have no clue lol

Answer 8

To convert to degrees we multiply by \(\large \frac{180}{\pi}\)

so

\[\large \frac{\pi}{6} \times \frac{180}{\pi}\]
\[\large \frac{180\cancel{\pi}}{6\cancel{\pi}}\]

so what is 180/6?

Answer 9

is it 30?

Answer 10

Right!

That, is what tells us which triangle to use, we use the triangle with 30 degrees in it

Answer 11

Ok i am following you

Answer 12

So now

We look at that triangle

Answer 13

WE need to focus on

the 30 degree mark

Answer 14

Now,

What does \(\large \cos\) equal? (in regards to right triangles)?

Answer 15

how do i figure that out? im sorry i know i am alot of trouble

Answer 16

No not at all, but I should assume that you have seen
\[\large \cos = \frac{adjacent}{hypotenuse}\] right?

Answer 17

yes but i dont remember how to figure it out

Answer 18

Oh, well there isn't exactly a way to figure it out...but there is a good way to remember the 3 basic trig functions

SOH-CAH-TOA

Think about it like this

Some Old Horse:

Sin
Opposite
Hypotenuse

Caught Another Horse:

Cos
Adjacent
Hypotenuse

Tripping On Acid:

Tan
Opposite
Adjacent

Good little memory thing there :)

Answer 19

i like that ^ lol :)

Answer 20

Good :) lol

Alright so with this

We know \[\large \cos = \frac{adjacent}{hypotenuse}\]

So from that angle...we need the side adjacent to that...and we need the hypotenuse of the triangle

Answer 21

So...since cos = adjacent/hypotenuse...

we will have

\[\large \cos = \frac{\sqrt{3}}{2}\]