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Problem 41

Solving a Trigonometric Equation In Exercises $3…

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Problem 40

Solving a Trigonometric Equation
In Exercises $35-42$ , solve the equation for $\theta,$ where $0 \leq \theta \leq 2 \pi$
$$\sin \theta=\cos \theta$$

Answer

$\theta=\frac{\pi}{4}, \frac{5 \pi}{4}$


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Video Transcript

problem Number 40 asks us to solve the equation. Signed data equals co signed data for theta, where data is less than equal to two pi, but greater than or equal to zero. No, When I think about a location on the unit circle where signed that equals coastline data, one angle measure comes to mind and that is pi forth and it's multiples. So right now I'm gonna go down and I'm gonna find high fourths and it's multiples on the unit circle. So you got pie fourths? Mmm pie forth in its, uh, multiples that air fractions of 1/4 is what I meant to say. I pray forthe in seven pair fourths now at the's values at the's Angle Measures Co Santa and Cynthia are all variations off square root too over too. All right, So for pine forest, it's square to over to screw to a tuber coast and sign at three. Power forth its negative squared over two square to over two for coastline and saying for five reports it's negative square to over two negative square to over two presenting coastline and then a seven power fourths. It's square to over two and negative square to over to co sign it. Sign now, Because we want to find a place where science data and concentrate are completely equivalent. We automatically see that the only location where that occurs is right here. Five pi fourths and read up Europe I fourth. And this behavior doesn't exist anywhere else on the unit circle. Um, so that's our answer. Fada equals hi forth and five pi fourths. Oops.

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