Linear Trig Equation Word Problem

aeromat · Nov 20, 2010

Homework Statement

Printed textbook problem 12: height h(t) = -4 sin(π/4 (t - 1)) + 2.5 metres of a nail in a water wheel over time t in seconds, asking when the nail is below water in the first 24 s.

Homework Equations

Reference card of three double angle formulas: sin 2θ = 2 sin θ cos θ; cos 2θ = cos²θ − sin²θ, = 2 cos²θ − 1, = 1 − 2 sin²θ; and tan 2θ = 2 tan θ / (1 − tan²θ).

Reference table of angle sum and difference formulas for sine, cosine and tangent: sin(a + b) = sin a cos b + cos a sin b, cos(a + b) = cos a cos b - sin a sin b, tan(a + b) = (tan a + tan b)/(1 - tan a tan b), with the subtraction versions beside them.

The Attempt at a Solution

The part I don't understand is what would be substituted (if anything) for the 24s? How will that be implemented to solve for the periods of time?

Mark44 · Nov 20, 2010

You aren't supposed to substitute anything for the 24 seconds. That is the domain for t in this problem. The problem is asking, for what values of t in [0, 24], is h(t) < 0.

aeromat · Nov 20, 2010

Ok so you would just graph it and use symmetry analysis to pick out the intervals right? Symmetry meaning look for radians that are equivalent in their values.

Mark44 · Nov 21, 2010

Graphing it would be a good start.

"Look for radians that are equivalent in their values." I don't know what that means.

Linear Trig Equation Word Problem

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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