Back to Prove and use Pythagorean identity — Problem 3 · Task Set 77

HSF.TF.C.8 Tutor Intake — Pythagorean Identity and Trig Values

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Grade 9·10 problems·~13 min·Common Core Math - HS Functions·group·hsf-tf-c-8

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Concepts

A student applies the Pythagorean identity and finds $\sin^2(\theta) = \dfrac{9}{25}$ .
The student writes $\sin(\theta) = \dfrac{3}{5}$ as the final answer. What is wrong
with this reasoning?

The student should have used $\cos^2(\theta) = 1 - \sin^2(\theta)$ instead

Taking a square root gives $\pm\dfrac{3}{5}$ ; without quadrant information,
both values are possible and the student must use the quadrant to choose the sign

The correct answer is $\sin(\theta) = \dfrac{\sqrt{9}}{\sqrt{25}} = \dfrac{3}{5}$ , so the student is right

The student confused $\sin^2(\theta)$ with $\sin(\theta^2)$