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owlet
 one year ago
Help me solve this please: \(\sf sin(cos^{1} (3/5))\)
owlet
 one year ago
Help me solve this please: \(\sf sin(cos^{1} (3/5))\)

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FibonacciChick666
 one year ago
Best ResponseYou've already chosen the best response.0So let's start with what will you do first?

FibonacciChick666
 one year ago
Best ResponseYou've already chosen the best response.0(by order of ops)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle \sin(\cos^{1}x)=\sqrt{1\left[\cos(\cos^{1}x)\right]^2~~} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1using, the fact that: sin²(w) + cos²(w) = 1 sin²(w) = 1  cos²(w) sin(w) = \(\sqrt{1  \cos^2(w)}\) in this case w is: \(\cos^{1}(3/5)\) (That makes it even easier for you)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1And also, you should know that: \(\large\color{black}{ \displaystyle \left[\cos(\cos^{1}\theta)\right]=\theta }\)

owlet
 one year ago
Best ResponseYou've already chosen the best response.0wait i'm confused.. why did you take the sqrt ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1because I had sin²(quantity) and I want to solve for just sin(quantity)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2Support @SolomonZelman \(\pm \sqrt...\)

FibonacciChick666
 one year ago
Best ResponseYou've already chosen the best response.0@SolomonZelman nice use of identity, but it's a special triangle. If one recognizes that it can be done in two steps

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Well, it is a number in our case, and I was assuming that just like by taking a square root of any ordinary number such as √35 you don't have a ±, so it would be here without a ±....

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(Well, it is a single value expression, isn't it ? )

owlet
 one year ago
Best ResponseYou've already chosen the best response.0@FibonacciChick666 my first attempt, I also used special triangles and the answer that I got is 4/5 but it's not right

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2cos (theta) = negative number, then theta can be in Quadrant 2 or Quadrant 3. That is why when taking off the square root, you need +/

owlet
 one year ago
Best ResponseYou've already chosen the best response.0okay, I understand that part, but how am I going to apply it to solve for cos^1 (3/5)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2\(cos (\alpha) = A \) that is \(cos^{1} A = \alpha\), right?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2Hence \(cos (\alpha) = 3/5= \dfrac{adj}{hypotenuse}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1owlet your answer, I think that should be positive.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2now, \(sin(\alpha) = \dfrac{opposite}{hypotenuse}= 4/5\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2However, when alpha is in Quadrant 3, you still have cos alpha = 3/5

FibonacciChick666
 one year ago
Best ResponseYou've already chosen the best response.0What loser is saying is what I was getting at

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2hence sin (alpha) = 4/5 also

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2Your answer should be both. I think!!

FibonacciChick666
 one year ago
Best ResponseYou've already chosen the best response.0I agree with Loser given no stipulations on quadrant

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1i checked wolfram gives only 4/5 positive. http://www.wolframalpha.com/input/?i=sin%28cos%5E%281%29+of+%283%2F5%29%29

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So it assumes that it is in the 2nd quadrant.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2@SolomonZelman It's nice but to us (@FibonacciChick666 and me) we need the firm logic to make sure that we don't miss any cases on our argument. :)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Sure, I am not against 4/5:)

owlet
 one year ago
Best ResponseYou've already chosen the best response.0i was doing the same thing as loser.. but yeah i think that the right answer is positive 4/5 but idk why the right is only positive

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2You may have some restriction on the problem, like the angle is in Q2. or (0, pi) for domain.
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