Back to Solve trigonometric equations — Problem 2 · Task Set 75

HSF.TF.B.7 Tutor Intake — Solving Trigonometric Equations in Context

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Grade 9·11 problems·~14 min·Common Core Math - HS Functions·group·hsf-tf-b-7

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Procedures

A temperature model gives $\sin\!\left(\dfrac{\pi t}{12}\right) = 0.5$
after isolation, where $t$ is hours after midnight.

A student applies arcsin and gets $\dfrac{\pi t}{12} \approx 0.5236$ .
They then report $t \approx 0.5236$ as the answer.

What error did the student make?

They used the wrong inverse function — they should have used arccos.

They forgot to solve for $t$ : the angle $\dfrac{\pi t}{12} \approx 0.5236$ ,
so $t = \dfrac{12(0.5236)}{\pi} \approx 2.0$ .

They found the principal value correctly; no error was made.

They should have added $2\pi$ to 0.5236 before solving for $t$ .