ACTUAL QUESTION: A weight is suspended on a vertical spring. The position x of the weight on the vertical number line is given by the function x= 3 sin (t) + 2 cos (t), where t is time in seconds. a. Find the initial position of the weight (its position at time t= 0). 7* b. Find the exact position of the weight at time t= seconds. a. The initial position of the weight is 2. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) b. The exact position of the weight at time t= seconds is O. et3D (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) A confusing start to an example: A weight is suspended on a vertical spring. The position x of the weight on the vertical number line is given by the function second-S., where t is time in seconds. a. Find the initial position of the weight (its position at time t= 0). b. Find the exact position of the weight at time t= 5 sin (t) + 7 cos (1) seconds. a. To find the initial position of the weight, substitute t = 0 into the given function for x, and evaluate. x= 5 sin (1) + 7 cos (1) =5 sin (0) + 7 cos (0) =5.0+7.1 -7 Replace t with 0. Evaluate sin o and cos 0. Simplify. Thus, the initial position of the weight is Line and Paragraph Spacing 7x 7x b. To find the exact position of the weight at time t=, substitute t= into the given function for x, and evaluate. x= 5 sin (t) +7 cos (t) 7x +7 cos 7x Replace t with =5 sin 7x depending on the quadrant in 7% and cos Evaluate sin 7x lies. Sketch the angle which the terminal side of in standard position.

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.