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nekit [7.7K]
3 years ago
11

Find the exact value of cos(arcsin(1/4)). For full credit, explain your reasoning.

Mathematics
1 answer:
Westkost [7]3 years ago
5 0
First way
arcsin(1/4) means that 1/4 sin of the angle.

sin(α)=1/4
sin²α+cos²α=1
(1/4)²+cos²α=1
cos²α=1-1/16 =15/16
cosα=+/-(√15)/4

<span>Second way
</span>
sin(α)=1/4 =opposite leg/hipotenuse
cos(α)=adjacent leg/hypothenuse
adjacent leg =√(hypotenuse²- Opposite²)=√(16-1)=√15
cosα=+/-√15/4

For one value of sinα, possible 2 values of cosα.

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pav-90 [236]
Well I don't know ! 
Let's take a look and see:

The idea is that there could be more than one way
for a roll of the dice to land with the same number.  

-- If the sum is from 1-4, you get the point.
There are  6  different ways for a roll of the dice to come up 1-4.

-- If the sum is from 5-8, Adam gets the point.
There are  20  different ways for a roll of the dice to come up 5-8.

-- If the sum is 9-12, Lana gets the point.
There are  10  different ways for a roll of the dice to come up 9-12.

-- The game is not fair to all three of you.
-- Lana has a distinct advantage over you.
-- Adam has a big advantage over Lana.
-- Adam has an even bigger advantage over you.
-- You are at a big disadvantage.  (Notice that one of your
numbers ... 1 ... can never come up unless one of the dice
falls off of the table.)
_______________________________

Here's how to figure it:

Ways to roll a 2:
1 ... 1

Ways to roll a 3:
1 ... 2
2 ... 1

Ways to roll a 4:
1 ... 3
2 ... 2
3 ... 1

Ways to roll a 5:
1 ... 4
2 ... 3
3 ... 2
4 ... 1

Ways to roll a 6:
1 ... 5
2 ... 4
3 ... 3
4 ... 2
5 ... 1

Ways to roll a 7:
1 ... 6
2 ... 5
3 ... 4
4 ... 3
5 ... 2
6 ... 1

Ways to roll an 8:
2 ... 6
3 ... 5
4 ... 4
5 ... 3
6 ... 2

Ways to roll a 9:
3 ... 6
4 ... 5
5 ... 4
6 ... 3

Ways to roll a 10:
4 ... 6
5 ... 5
6 ... 4

Ways to roll 11:
5 ... 6
6 ... 5

Ways to roll 12:
6 ... 6

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iogann1982 [59]
I think this is how u start it

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