SOLUTION: A is an angle in quadrant 2. TanA = -3/root5. Solve the following and rationalize the denominator to the exact value. a) Sin2A b) Cos 2A c) Cos(A + pi/2) d) Sin(A + pi/2)

Question 1030548: A is an angle in quadrant 2. TanA = -3/root5. Solve the following and rationalize the denominator to the exact value.
a) Sin2A
b) Cos 2A
c) Cos(A + pi/2)
d) Sin(A + pi/2)
Answer by ikleyn(52804) (Show Source): You can put this solution on YOUR website!
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A is an angle in quadrant 2. TanA = -3/root5. Solve the following and rationalize the denominator to the exact value.
a) Sin2A
b) Cos 2A
c) Cos(A + pi/2)
d) Sin(A + pi/2)
~~~~~~~~~~~~~~~~~~~~~~~~~~~

First of all, we need to find  sin(A)  and  cos(A)  based on the given value of tan(A) and the fact that angle A is in quadrant 2.

For it, we will use well known formulas  of Trigonometry 

 =   and   = .


Since tan(A) = , we have 
sin(A) =  =  =  =  =      and 


cos(A) = - = - = - = - = .


The sign for sin(A) is "+" since the angle A is in Q2.  The sign for cos(A) is "-" due to the same reason.


Now

a)  sin(2A) = 2*sin(a)*cos(A) =  =  =  = .

b)  cos(2A) =  =  =  = .

    (By the way, the fact that cos(2A) is negative means that the angle 2A is in Q3).


c)  cos(A + pi/2) = -sin(A) = -.

d)  sin(A + pi/2) = cos(A) = .

The problem is solved.

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