The intervals apply to the x column. And f(x) is just a different way of saying y. So when y is greater than 0 on the chart, what is true about x. So far as I can tell, the second and last choices are correct.
Step-by-step explanation:
(2)
cos(2θ) tan θ + sin θ = 0
tan θ (cos(2θ) + cos θ) = 0
tan θ = 0
θ = kπ
cos(2θ) + cos θ = 0
cos(2θ) = -cos θ
cos(2θ) = cos(π − θ)
2θ = π − θ + 2kπ
3θ = (2k + 1) π
θ = (2k + 1) π / 3
Therefore, θ = kπ or (2k + 1) π / 3.
(3)
2 cos² θ − 2 cos²(2θ)
Power reduction formula:
1 + cos(2θ) − (1 + cos(4θ))
cos(2θ) − cos(4θ)
Y=7/4x+9/7 is an equation perpendicular to that
This is a polynomial with more than 2 as a degree. Using Descartes Rule of Signs:
f(x) = x⁶ + x⁵ + x⁴ + 4x³ − 12x² + 12
Signs: + + + + − + 2 sign changes ----> 2 or 0 positive roots
f(−x) = (−x)⁶ + (−x)⁵ + (−x)⁴ + 4(−x)³ − 12(−x)² + 12 f(−x) = x⁶ − x⁵ + x⁴ − 4x³ − 12x² + 12
Signs: + − + − − + 4 sign changes ----> 4 or 2 or 0 negative roots
Complex roots = 0, 2, 4, or 6