Back to Solve trigonometric equations — Problem 4 · Task Set 76

Exercises: Solve Trigonometric Equations

Use radian mode on your calculator throughout. Show all steps.

Grade 9·23 problems·~30 min·Common Core Math - HS Functions·group·hsf-tf-b-7

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Fluency Practice

You found $\sin(\pi t/4) = 0.75$ , and the principal solution gives $\pi t/4 \approx 0.8481$ .

Within one period of length 8 (since the period is $2\pi / (\pi/4) = 8$ ), there is a second value of $\pi t/4$ that also gives $\sin = 0.75$ . What is it?

$\pi - 0.8481 \approx 2.2935$ (supplementary angle, since sine is symmetric about $\pi/2$ )

$2\pi - 0.8481 \approx 5.4351$ (wrong symmetry — this applies to cosine, not sine)

$0.8481 + \pi \approx 3.9897$ (this would give a negative sine value)

There is only one value — the calculator gives the complete answer.