Question

Can someone help me evaluate this problem? http://gyazo.com/46a13ac3f1a150ff10c3af4fa3d28223

Answer 1

change cot to cos/sin
and if you are fuzzy about radians, change the angle to degrees
It looks like it will be a "standard" angle

Answer 2

How will the problem look if it was cos/sin then? I'm lost. @phi

Answer 3

do you know what tan is using sin and cos ?

Answer 4

I probably do, just need to refresh my memory.

Will I have to do a^2 + b^2 = c^2? to find r?

Answer 5

first things first... how do you write tan x using sin x and cos x ?

Answer 6

No idea.

Answer 7

do you know the definition of tan from SOH CAH TOA ?

Answer 8

yeah opposite over adjacent

Answer 9

you know sin = o/h and cos = a/h
what do you get if you mulltiply o/h * h/a ?

Answer 10

I don't get what you just asked.

Answer 11

\[ \frac{o}{h} \cdot \frac{h}{a} \]

Answer 12

can you simplify that ?

Answer 13

o/a?

Answer 14

could you simplify
\[ \frac{2 \cdot 3}{4\cdot 2} \]?

yes o/a
(the h's cancel)

now o/a is tan, right ?
so you know
o/h * h/a = tan
what is o/h ?
any idea what h/a is ?

Answer 15

h/a is cos right?

Answer 16

almost

Answer 17

o/h is sin

Answer 18

no h/a is called secant, but it's easier to just remember it's cos "flipped"

Answer 19

Oh oh okay.

Answer 20

in other words , if
\[ \cos x = \frac{a}{h} \\ \frac{1}{\cos x} = \frac{h}{a} \]

now look back at what we know
o/h * h/a = o/a
sin * 1/cos = tan

in other words
\[ \frac{\sin x}{\cos x} = \tan x \]

by definition cotangent is 1/tan

Answer 21

if you have cot x
can you write that using sin and cos ?

Answer 22

so cos/sin = 1/tan?

Answer 23

yes

now let's answer the question
do you know how to change radians to degrees?
you multiply by 180/pi and simplify
can you do that for this problem ?

Answer 24

so -3pi/2 * 180/pi?

Answer 25

yes

Answer 26

270

Answer 27

what happened to the - sign ?

Answer 28

-270

Answer 29

the minus means we start at the x-axis and go clockwise
around the circle.

any idea where we end up ?

Answer 30

Wait no first right?

Answer 31

imagine standing at the origin, looking along the x-axis.
turn clockwise 90 degrees (that means your turned -90 degrees)
any idea which way you are looking ?

Answer 32

down?

Answer 33

yes. now turn another -90. where are you looking ?

Answer 34

-x - axis

Answer 35

so far we have turned -180
one more -90
which way are we looking ?

Answer 36

y axis

Answer 37

yes, here is the picture