Final answer:
To eliminate the parameter with sin and cos, use trigonometric identities to express one function in terms of the other and simplify.
Step-by-step explanation:
Eliminating the Parameter with Sin and CosTo eliminate the parameter in equations involving sin and cos, we often use trigonometric identities. For example, the identity for tan θ as sin θ/cos θ can simplify expressions where both sine and cosine are present, and terms may cancel out. Consider the trigonometric identity cos2 θ = 1 - sin2 θ or sin2 θ = 1 - cos2 θ to substitute one function for another in equations to resolve them into a single trigonometric function.When given a parametric equation in terms of sin and cos, such as describing the motion on a circular path or oscillation like y (x, t) = A sin (Bx + C) cos (Dt), applying these identities simplifies the expression and eliminates the dependence on the parameter t or xTo eliminate the parameter with sin and cos, we can use trigonometric identities and substitutions.
For example, if we have an equation involving both sin and cos, we can substitute sin²θ for 1 - cos²θ or cos²θ for 1 - sin²θ. This allows us to write the equation in terms of only sin or cos, eliminating the parameter.However, the exact method for eliminating the parameter depends on the form of the equation and the relationship between the functions. By substituting with equivalent expressions or utilizing identities like double-angle identities or sum-to-product formulas, such as cos 2θ = cos2 θ - sin2 θ, it is possible to rewrite the equation in terms of a single variable or function.