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Mathematics 16 Online
OpenStudy (anonymous):

What is 2 pi/5 radians in degrees?

OpenStudy (anonymous):

72 degrees

OpenStudy (anonymous):

because you change pi radians to 180 degrees, so 2(180)/5 = 72

OpenStudy (anonymous):

Thanks! The point (3, -4) is on the terminal side of an angle 0 . What is cos 0 ?

OpenStudy (gorv):

(180/pi ) *(2pi/5)=72 degree

OpenStudy (anonymous):

cos theta = 3/5

OpenStudy (anonymous):

use (pi) radians = 180 degrees

OpenStudy (anonymous):

becuase you draw the right triangle in quadrant IV, you see that the hypotenuse is 5 from Pythagorean Theorem

OpenStudy (anonymous):

If tan 0 =12/5 and cos 0 < 0, what is sin 0 ?

OpenStudy (anonymous):

lol

OpenStudy (anonymous):

sin theta = 5/13

OpenStudy (anonymous):

draw the 5-12-13 triangle

OpenStudy (anonymous):

you are a genius

OpenStudy (anonymous):

What is tan 3pi/2 ?

OpenStudy (anonymous):

that is tan (120) = - tan 60 = - sqrt(3)

OpenStudy (anonymous):

Note: error

OpenStudy (anonymous):

that is tan (270) which is undefined

OpenStudy (anonymous):

3pi/2 = 3(180)/2 = 270

OpenStudy (anonymous):

so tan (270) is undefined.

OpenStudy (anonymous):

What is the reference angle for 120°?

OpenStudy (anonymous):

60?

OpenStudy (anonymous):

It is 60 degrees.

OpenStudy (anonymous):

Which expression is equivalent to (1 – sin2 x)(sec x)?

OpenStudy (anonymous):

you are currently helping me graduate high school! THANK YOU!

OpenStudy (anonymous):

welcome.

OpenStudy (anonymous):

(1-sin^2x) = cos^2 (x) so you have cos^2(x)(sec x) = cos x Reason is that sec x = 1/cos x and you should know that 1- sin^2(x) = cos^2(x)

OpenStudy (anonymous):

Final answer is cos x as I showed above.

OpenStudy (anonymous):

Which expression is equivalent to cot t sec t?

OpenStudy (anonymous):

csc t, sin t, tan t, sin^2 t, csc^2 t ?

OpenStudy (anonymous):

cot t = cos t/sin t and sec t = 1/cos t so cot t sect t = (cos t/sin t) times 1/cos t = 1/sin t = csc t

OpenStudy (anonymous):

it's csc t?

OpenStudy (anonymous):

yes

OpenStudy (anonymous):

Which function has a phase shift of pi/2 the right?

OpenStudy (anonymous):

choices?

OpenStudy (anonymous):

one second

OpenStudy (anonymous):

I assume you are looking for cos x

OpenStudy (anonymous):

because when you shift sin x pi/2 to the right you get cos x

OpenStudy (anonymous):

y = 2sin(1/2x+pi), y = 2sin(2x +pi), y = 2sin(x +pi/2),y = 2sin(x -pi) , y = 2sin(2x -pi)

OpenStudy (anonymous):

each options is separated by commas

OpenStudy (anonymous):

y = 2sin((x+pi/2)

OpenStudy (anonymous):

x + pi/2 = 0 gives you x = -pi/2

OpenStudy (anonymous):

What is the domain of y = cot x?

OpenStudy (anonymous):

x cannot be 0,180, 360 or any multiple of 180

OpenStudy (anonymous):

because cot x = cos x/sin x so a fraction is undefined when the denominator is zero sin x = 0 when x = 0, 180, 360, etc...

OpenStudy (anonymous):

none of my options are 'undefined'

OpenStudy (anonymous):

(-infinity, infinity), (0, pi), all x= pi/2+pi, all x= pi, all x=pi/2

OpenStudy (anonymous):

those are my options

OpenStudy (anonymous):

poorly written choices

OpenStudy (anonymous):

You want the domain...the domain is all possible values that x can be

OpenStudy (anonymous):

the best choice would be (0,pi)

OpenStudy (anonymous):

domain exists on (0,pi)

OpenStudy (anonymous):

yeah this things sucks. .. Simplify the expression: 1/1+cot^2 x

OpenStudy (anonymous):

1 + cot^2(x) = csc^2(x)...

OpenStudy (anonymous):

so 1/csc^2(x) = sin^2(x)

OpenStudy (anonymous):

Final answer is sin^2(x)

OpenStudy (anonymous):

Makes sense?

OpenStudy (anonymous):

Given tan 0= 4/3 and sin=(-4/5), find cos 0

OpenStudy (anonymous):

yeah. how are you so good at this?

OpenStudy (anonymous):

tan theta = sin theta/cos theta so, 4/3 = -4/5/cos theta so cos theta = - 3/5

OpenStudy (anonymous):

got it?

OpenStudy (anonymous):

Solve 2cos2x + cosx − 1 = 0 for x over the interval [0, 2.pi. yes!

OpenStudy (anonymous):

This is a trig equation..I will work it out step-by-step...watch

OpenStudy (anonymous):

k

OpenStudy (anonymous):

are you a math teacher?

OpenStudy (anonymous):

We first factor: (2cos x - 1)(cos x + 1) = 0 Set each factor equal to 0, we get: 2 cos x - 1= 0, so cos x = 1/2, and x = pi/3 and 5pi/3 cos x + 1 = 0, so cos x = -1, so x = pi

OpenStudy (anonymous):

x = pi/3, pi, and 5pi/3

OpenStudy (anonymous):

makes sense

OpenStudy (anonymous):

Do you understand?

OpenStudy (anonymous):

yes.. this is the last one to my test.... Which expression is equivalent to tan(-x)cos2x?

OpenStudy (anonymous):

choices?

OpenStudy (anonymous):

-sin xcos x, sin xcos x, tan x + sin2x, tan x − sin2x, -tan x − sin2x

OpenStudy (anonymous):

tan(-x) = - tan x cos(2x) = many formulas.. Are you typing your question correctly? I dont see it

OpenStudy (anonymous):

check the question again

OpenStudy (anonymous):

yeah.. I even copied and pasted it

OpenStudy (anonymous):

I cant open the document

OpenStudy (anonymous):

is it cos(2x) or cos^2(x) in your question?

OpenStudy (anonymous):

oooh you know why because all of the options are supposed to be a ^ in front of the 2

OpenStudy (anonymous):

oh...see, I told you something was wrong

OpenStudy (anonymous):

so retype your question and the choices

OpenStudy (anonymous):

I'll be back in 3 minutes...will see your question and choices when I return

OpenStudy (anonymous):

Which expression is equivalent to tan(-x)cos2x? -sin xcos x sin xcos x tan x + sin^2x tan x − sin^2x -tan x − sin^2x

OpenStudy (anonymous):

sorry...I still dont see it. Assuming you typed the question correctly.

OpenStudy (anonymous):

I believe there's an error in the question

OpenStudy (anonymous):

Or I just dont see it

OpenStudy (anonymous):

what do you think the closest option is?

OpenStudy (anonymous):

we do know that, tan(-x) = - tan x

OpenStudy (anonymous):

and we know that cos(2x) = 2 cos^2(x) - 1 or 1 - 2 sin^2(x)

OpenStudy (anonymous):

In this type of question, I cannot eliminate any choice

OpenStudy (anonymous):

so it's one of the tans?

OpenStudy (anonymous):

I dont want to second guess

OpenStudy (anonymous):

Not necessarily..could be any of the choices...are you sure that you typed the question correctly?

OpenStudy (anonymous):

Or just post this question, maybe someone will see it.

OpenStudy (anonymous):

I think you meant cos^2(x) in the question!

OpenStudy (anonymous):

you typed cos (2x)

OpenStudy (anonymous):

If it's cos^2x, then its easy

OpenStudy (anonymous):

If it's cos^2(x), then it is - sin x cos x

OpenStudy (anonymous):

are you there?

OpenStudy (anonymous):

Thanks!

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