SOLUTION: Please help me with this question,If SinA=2/3,and A is obtuse, find the exact value of, 1)CosA, 2)sin2A, 3) tan2A

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me with this question,If SinA=2/3,and A is obtuse, find the exact value of, 1)CosA, 2)sin2A, 3) tan2A      Log On


   

Question 1190009: Please help me with this question,If SinA=2/3,and A is obtuse, find the exact value of,
1)CosA, 2)sin2A, 3) tan2A
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
sin%28A%29=2%2F3+and A is obtuse
if sin%28A%29=2%2F3+ than
A=sin%5E-1%282%2F3%29
A=138.19° (obtuse)

if
sin%28A%29=2%2F3+=> opp%2Fhyp=2%2F3+=> opp=2, hyp=3
than adj=sqrt%283%5E2-2%5E2%29=sqrt%285%29


1)
cos%28A%29=sqrt%285%29%2F3

2)
sin%282A%29=2+sin%28A%29+cos%28A%29

sin%282A%29=2%282%2F3%29+%28sqrt%285%29%2F3%29

sin%282A%29=%284sqrt%285%29%29%2F9


3)
tan%282A%29=%282sin%28A%29cos%28A%29%29%2F%28cos%5E2%28A%29+-+sin%5E2%28A%29%29



tan%282A%29=%28%284sqrt%285%29%29%2F9%29%2F%281%2F9%29

tan%282A%29=4sqrt%285%29


Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
Please help me with this question, If SinA=2/3,and A is obtuse, find the exact value of,
1)cosA, 2)sin2A, 3) tan2A
~~~~~~~~~~~~~~~~


            The solution by @MathLover1 is  INCORRECT.

            I came to bring a correct solution. 


(1)  cos(A) = -sqrt%281-sin%5E2%28A%29%29 = -sqrt%281+-+%282%2F3%29%5E2%29 = -sqrt%281-4%2F9%29 = -sqrt%285%2F9%29 = -sqrt%285%29%2F3.


     Since A is obtuse, angle A is in QII, where cosine is negative, so we use sign  " - "  at the square root.


     It is first difference from the solution by @MathLover1.




(2)  sin(2A) = 2*sin(A)*cos(A) = 2%2A%282%2F3%29%2A%28-sqrt%285%29%2F3%29 = -%284%2Asqrt%285%29%29%2F9.


     Notice sign  " - " in my answer.  It is the second difference from the solution by @MathLover1.




(3)  tan(2A) = sin%282A%29%2Fcos%282A%29 = sin%282A%29%2F%28cos%5E2%28A%29+-+sin%5E2%28A%29%29 =  +%28%28-4%2Asqrt%285%29%2F9%29%29%2F%28%28-sqrt%285%29%2F3%29%5E2+-+%282%2F3%29%5E2%29 = %28%28-4%2Asqrt%285%29%2F9%29%29%2F%28%285%2F9+-+4%2F9%29%29 = %28%28-4%2Asqrt%285%29%2F9%29%29%2F%28%281%2F9%29%29 = -4%2Asqrt%285%29.


     Notice sign  " - " in my answer.  It is the third difference from the solution by @MathLover1.

Solved     (correctly).