Question 1113961: The three numbers (1/24)sinA, (1/3), and TanA are in geometric progression. Find the numerical value of cosA, where 0° < A < 90°.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The three numbers (1/24)sinA, (1/3), and TanA are in geometric progression. Find the numerical value of cosA, where 0° < A < 90°.
-------------
Equation::
(1/3)/[(1/24)sin(A)] = [tan(A)/(1/3)]
---------
Cross-multiply
(1/24)sin(A)*tan(A) = 1/9
------
[sin^2(A)/cos(A)] = (1/9)/(1/24)
-------
(1-cos^2(A))/cos(A) = (8/3)
-----
3-3cos^2(A)- 8cos(A) = 0
-----
3cos^2(A) + 8cos(A) -3 = 0
-------
cos(A) = [-8+-sqrt(64-4*3*-3)]/(2*3)
Positive answer = 2/(2*3) = 1/3
Negative answer = -18/(6) = -3 (not acceptable for cosine value)
===========
Cheers,
Stan H.
-----------
|
|
|
