Question 1158249: Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.)
sin(θ) = − sqr2/2
Found 2 solutions by Theo, josmiceli:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! sin(theta) = -sqrt(2)/2
to find the equivalent angle in the first quadrant, solve for sin(theta) = sqrt(2)/2
that makes theta equal to 45 degrees.
the sine of 45 degrees is positive in the first quadrant and the second quadrant.
it is negative in the third quadrant and the fourth quadrant.
therefore, for 0 <= x <= 360 degrees, the angle will be:
180 + 45 = 225 degrees in the third quadrant.
360 - 45 = 315 degrees in the fourth quadrant.
this repeats every 360 degrees, therefore, the complete answer is:
225 plus or minus k * 360 degrees and 315 plus or minus k * 360 degrees.
i don't remember, and i can't find the reference, but this may be able to be written as {225,315} plus or minus k * 360.
on a graph, this would look like this.
the example shows that y = -sqrt(2)/2 occurs at:
225 degrees and 315 degrees when k = 1
1305 degrees and 1390 degrees when k = 3
-855 degrees and -765 degrees when -k = -3
the sine wave function repeats forever in each direction every 360 degrees.
Answer by josmiceli(19441)  (Show Source):
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