Question 613680: General Degree Solution √2secΘ + 2tanΘ = 0
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i get x = 225 or 315 when 0 <= x <= 360 degrees.
if your domain is not restricted, then the answer would be:
x = 225 +/- 360*n and x = 315 +/- 360*n
this is because the sin is negative in the third and fourth quadrant.
i solved as follows:
sqrt(2)*sec(x) + 2*tan(x) = 0
since sec(x) is equal to 1/cos(x) and tan(x) is equal to sin(x)/cos(x), the equation becomes:
sqrt(2)/cos(x) + 2*sin(x)/cos(x) = 0
since the denominator is the same, you can combine the 2 terms to get:
(sqrt(2) + 2*sin(x)) / cos(x) = 0
multiply both sides of the equation by cos(x) to get:
sqrt(2) + 2*sin(x) = 0
subtract sqrt(2) from both sides of the equation to get:
2*sin(x) = -sqrt(2)
divide both sides of the equation by 2 to get:
sin(x) = -sqrt(2)/2
since sin(45) = sqrt(2)/2 and sine is negative in the third and fourth quadrant, then the angle must be 225 degrees (third quadrant) or 315 degrees (fourth quadrant).
since the sine and cosine functions are repetitive every 360 degrees, then you'll get the same sine every multiple of 360 degrees.
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