Question

5 cos(9ω)=4+7 [cos(5θ)]² defines an implicit relationship between ω and θ. Use implict differentiation to find a formula for dω/dθ in terms of ω and θ. The formula will have the form dω/dθ = K cos(5θ)/sin(9ω) Where K is a constant what is the value of K?

Answer 1

To find the formula for dω/dθ in terms of ω and θ, we can use implicit differentiation. The formula for dω/dθ is dω/dθ = 14cos(5θ)/sin(9ω), where K is equal to 14.

Step-by-step explanation:

To find the formula for ∅ω/∅θ in terms of ω and θ, we need to use implicit differentiation. We have the equation 5cos(9ω) = 4 + 7[cos(5θ)]². Differentiating both sides of the equation with respect to θ, we get -45sin(9ω)∅ω = 14cos(5θ)sin(5θ)∅θ. Rearranging the equation, we get -45sin(9ω)∅ω = 14cos(5θ)sin(5θ)∅θ. Dividing both sides by cos(5θ)sin(9ω), we get -45∅ω/sin(9ω) = 14∅θ/cos(5θ). Thus, the formula for ∅ω/∅θ in terms of ω and θ is dω/dθ = 14cos(5θ)/sin(9ω). Therefore, the value of K is 14.