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sin is the y axle :

Q2. | Q1

..+...|.. +

____| ___

.. - ..| -

.Q3 | Q4

So is positive in Q1 e Q2 and negative in Q3 e Q4

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cos is the x axle ...

So

Q2 | Q1

..-..|.. +

___| ___

..-..| +

.Q3 | Q4

is positive in Q1 e Q4 and negative in Q2 e Q3.

Answering your question:"in quadrant2 cos x will be negative right? " Yes, it´s right.

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Well I think you mixed the variables ... Do you want know what is cos α/2 if sin α = 3/5?

If it is...

sin ² α + cos ² α = 1

(3/5)² + cos ² α = 1

(9/25) + cos ² α = 1

cos ² α = 1 - 9/25

cos ² α = 16/25

cos α = √(16/25)

α is in Q2, so cos α is negative :

cos ² α = -4/5

cos α/2 = √((1+cos α)/2)

cos α/2 = √((1-4/5)/2)

cos α/2 = √((1/5)/2)

cos α/2 = √((1/5)*1/2)

cos α/2 = √(1/10)

Note that if α is in Q2:

90º<=α<=180º

Dividing by 2:

90º/2 <=α/ 2<=180º/2

45º <=α/ 2<=90º

So α/2 is in Q1 and cos α/2 is positive:

cos α/2 = 1/√10

cos α/2 = 1√10/√10√10

cos α/2 = √10/10

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Sorry for my bad english...

I hope you can understand.

Kisses from Brazil

=**

If sin x = 3/5, then it will be in Q1 or Q2. Or, we could say, 0<=X<=180

and 0<=X/2<=90

So X/2 will be in Q1.

So cos X/2 will be positive.

I feel you cannot find cos [alpha/2] No matter what sinx is.

Did you mean cos(x/2)?

Type carefully now onwards!!!!