Solve this equation for 0º≤θ≤360º.
A) 45º; 135º; 225º
B) 45º; 90º; 270º; 315º
C) 45º; 135º; 225º; 315º
D) 45º; 135º
+130466 Notice that the only thing that can make this 0 is when the numerator on the left side = 0
So
cos 2Θ = 0
And the cosine is equal to 0 at 90, 270, 450 and 630 degrees......so dividing each by 2, we have
45, 135, 225 and 315 degrees.......(and notice that the sin ≠ 0 at any of these values, so the denominator of the fraction isn't 0 at any of these values, either !!!)
+23254 cos(2θ) / sin²(θ) = 0
cos(2θ) = cos²(θ) - sin²(θ)
[cos²(θ) - sin²(θ)] / sin²(θ) = 0 Use the substitution.
cos²(θ) / sin²(θ) - sin²(θ) / sin²(θ) = 0 Divide the numerator into two parts.
cos²(θ) / sin²(θ) - 1 = 0
cos²(θ) / sin²(θ) = 1
sin²(θ) / cos²(θ) = 1 Multiply both sides by sin²(θ) / cos²(θ) and exchange sides.
tan²(θ) = 1
tan(θ) = 1 ---> θ = 45° or 225°
tan(θ) = -1 ---> θ = 135° or 315°
+130466 Notice that the only thing that can make this 0 is when the numerator on the left side = 0
So
cos 2Θ = 0
And the cosine is equal to 0 at 90, 270, 450 and 630 degrees......so dividing each by 2, we have
45, 135, 225 and 315 degrees.......(and notice that the sin ≠ 0 at any of these values, so the denominator of the fraction isn't 0 at any of these values, either !!!)
