Question

4.) When Ⓗ=5π/6, what are the reference angle and sign values for sine, cosine and tangent?

5.) If sin Ⓗ=2/3 and tan Ⓗ<0, what is the value of cos Ⓗ ?

Answer 1

Okay first one

5pi/6=150 degrees.

That is in the 2nd quadrant.

reference angle=180-150=30 degrees

that's a simple 30-60-90 triangle, can you finish it?

Answer 2

And for the 2nd one

if sin=2/3

that is


use the pythagorean theorem to get the missing side.

then just remember that

tan=opp/adj

Answer 3

ok, i do not understand what you did for the first one, i only understood up to the part where it is located in the second quadrant

Answer 4

@dtan5457

Answer 5

You know that 5pi/6=150 degrees right?

Answer 6

Just making sure you understand the conversions.

Answer 7

@hailhydra

Answer 8

yeah, i look it up on the wheel and it gives that it is equal to 150 degrees

Answer 9

Okay. Now, whenever they give you a degrees...and you want to get the reference angle.

Refer to this.

In this case, 150 degrees is in the 2nd quadrant right?

so 180-150=30 degrees, your reference angle.

So far so good/

Answer 10

so, i use the reference angle formula for the second quadrant? if so, the Ө is where i plug in the 150?

Answer 11

@dtan5457

Answer 12

Yes

Answer 13

So your reference angle=..?

Answer 14

would it be...

Answer 15

Don't make it more hard than it needs to be, lol.

It's literally 180-150=reference angle

Answer 16

oh, but thats not an option that i have

Answer 17

Actually, give me your answer choice. I'm confusing myself.

Answer 18

ions are :

Answer 19

options are those

Answer 20

Oh, it's still 30 degrees.

Just convert 30 degrees to radians.

Answer 21

Know how to do that?

Answer 22

pie over 6?

Answer 23

Yes!

Answer 24

is it c?

Answer 25

because i know that in the second quadrant only sine is positive, right?

Answer 26

So, it looks like you don't even have to solve the triangle, you just need to do know which functions are positive and negative.

Answer 27

Correct. It is C.

Answer 28

yay!~~

can you help me with the second one aswell?

Answer 29

Absolutely.

If sin=2/3

Your triangle looks like this, solve using the pythagorean theorem.

Answer 30

a^2+b^2=c^2

Answer 31

so is it: 3^2+2^2=c^2 ?

Answer 32

Well, c^2 is already solved, that is your hypotenuse.

a^2+2^2=3^2

Answer 33

oh lol

Answer 34

so, we solve for a right?

Answer 35

a^2*

Answer 36

Yep

Answer 37

so i got this so far:

a^2+4+9

Answer 38

lol what xD

Answer 39

a^2+4=9 seems more right

Answer 40

so i dont solve 2^2 and 3^3 ? lol

Answer 41

ok ok so, the triangle is 90 degrees right? since its a right angle?

Answer 42

im trying to remember lol

Answer 43

Yep, otherwise we couldn't use the pythagorean theorem.

Answer 44

you still have to solve for a lol

Answer 45

ok, so ...i give up lol how do i solve for a?

Answer 46

a^2+4=9

what plus 4=9?

Answer 47

come on now...lol

Answer 48

is it 5? lol

Answer 49

I believe 4+5=9

so yes, it's 5.

now since it's a^2

it's \[\sqrt{5}\]

Answer 50

so a = 5?

Answer 51

Square root of 5, not 5.

Answer 52

Now that you have the full triangle..