M.SRM.30
Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.
Example Problems
The displacement in µm of a loudspeaker diaphragm can be modeled by:
At s the diaphragm passes through equilibrium moving outward, and 0.001 s later it reaches its first maximum of 0.008 µm.
Find , where t is in radians.
At s the diaphragm passes through equilibrium moving outward, and 0.001 s later it reaches its first maximum of 0.008 µm.
Find , where t is in radians.
A rotating lighthouse beam shines on a distant sensor. The light intensity in arbitrary units can be modeled by:
At s the intensity is (maximum). Two-and-a-half seconds later it falls to (minimum).
Find , where is in radians.
At s the intensity is (maximum). Two-and-a-half seconds later it falls to (minimum).
Find , where is in radians.
A mass on a spring oscillates horizontally. Its displacement in m from equilibrium can be modeled by:
At s the mass is at maximum extension, 0.15 m. It first passes equilibrium 0.4 s later.
Find , where is in radians.
At s the mass is at maximum extension, 0.15 m. It first passes equilibrium 0.4 s later.
Find , where is in radians.
Khan Academy ResourcesEvaluate inverse trig functionsInterpret solutions of trigonometric equations in contextSolve sinusoidal equations (basic)Sinusoidal models word problemsSolve sinusoidal equationsSine equation algebraic solution setCosine equation solution set in an intervalCosine equation algebraic solution setInterpreting solutions of trigonometric equations
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