Question

SAT Math Level 2 Question
The answer is D, but how do you get it?

I know that 1 - cos = sin

Answer 1

yeah what is it :3

Answer 2

If \[\frac{ 1-\cos \theta }{ \sin \theta } = \frac{ \sqrt{3} }{ 3 }\] then, theta =
(A) 15
(B) 30
(C) 45
(D) 60
(E) 75

Answer 3

C

Answer 4

@123AB456C Wrong.

Answer 5

This link provides solve with full steps for your question look at it :)
http://www.wolframalpha.com/input/?i=%7B%281-cos%28x%29%29%2Fsin%28x%29+%3D+sqrt%283%29%2F3%2C+0%3C%3D+x%2C+x+%3C%3D2pi%7D

Answer 6

the answer is 60 which is choice C

Answer 7

like your multiplication tables,
u need to memorize the values for cos and sin for the angles 0,30,60,90

Answer 8

add 45 degrees also to that list :)

Answer 9

@Albert0898 i guess you didn't look at the link i posted earlier , right?

Answer 10

@HossamHoussien I did, but I still don't get how that equation simplified. Although it's the right answer, I have no idea how the steps were computed. I've went through every rule and can't seem to simplify it the way Wolfram did.

Answer 11

Firstly you should notice that \[\frac{ \sqrt{3} }{ 3 }=\frac{ 1 }{ \sqrt{3} }\]
and according to "Half-angel formula"
it says that :
\[\tan (\frac{ x }{ 2 })=\frac{ 1-\cos(\theta) }{ \sin(\theta) }\]
So:
\[\tan (\frac{ x }{ 2 }) = \frac{ \sqrt{3} }{ 3 }\]
But you have to find value of (x) not (x/2)
By calculator \[\frac{ x }{ 2 }=\tan^{-1} (\frac{ 1 }{ \sqrt3 })\]
\[\frac{ x }{ 2 }=30\]
\[x=60\]
I hope that help