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University of California, Berkeley

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Problem 23

Evaluating Trigonometric Functions In Exerrises $21-24$ , evaluate the sine, cosine, and tangent of each angle. Do not use a calculator.

$$\begin{array}{ll}{\text { (a) } 225^{\circ}} & {\text { (b) }-225^{\circ}} & {\text { (c) } \frac{5 \pi}{3}} & {\text { (d) } \frac{11 \pi}{6}}\end{array}$$

Answer

(a) $1$

(b) $-\frac{1}{\sqrt{2}}$

(c) $-\sqrt{3}$

(d) $-\frac{1}{\sqrt{3}}$

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## Discussion

## Video Transcript

Okay, So 25 degrees is this. I'm great. Here are opposite. And Jake Insides are insane. And I have probably recruited to that. We have sign of 25 That's equal to negative or no risk. Reverted to coastline is the same thing. An intendant of 25 a be quick to opposite over adjacent Gives me one. Now for part B, we have negative to 25. I agree. Well, if this angle right here to 25 degrees in the negative event would be in question. So we have, uh I'm going with you. Our aviation and opposite sides of the same Well, And then I heard a pop the sign of 25 or negative 25. You could put one over square root of co sign and later to 25 years he quit to Livorno, discredited you intendant of negative 25. If you could see one over negative one, which gives me a negative one now for part C, the five pilots agree. Well, five pile of the three. Where is that? That is in quadrant more So we have. Hi. Okay, So this this angry cares about 60 the great. So are opposite sides largest that square with three negative of it. Um, are Jason sightings have been one. My practice is to So then sign a beta if we could to through three negatives over too. Co sign of data is equal to one over to intendant of data nuclear tuning descriptively over one. Now for Part B, we have 11 pie. Oh, sick 11 pie or six is close to 12 pi over six, which is to pine. So it's a little before or it's in Cordiant's for So we have 11 pi over angle right. Here's 30 degrees. So are opposite side is small angles, So this is a good one. Growing in 32 The sign of beta is equal to native one over two co sign a bit up. Is it a two for 123 over two intendant of better is it would seem that one over two. Actually, no scratch that it's opposite with your fate of one over adjacent, Would you square root of three

## Recommended Questions

Evaluating Trigonometric Functions In Exerrises $21-24$ , evaluate the sine, cosine, and tangent of each angle. Do not use a calculator.

$$\begin{array}{lll}{(a)-30^{\circ}} & {\text { (b) } 150^{\circ}} & {\text { (c) }-\frac{\pi}{6}} & {\text { (d) } \frac{\pi}{2}}\end{array}$$

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Evaluating Trigonometric Functions In Exerrises $21-24$ , evaluate the sine, cosine, and tangent of each angle. Do not use a calculator.

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Evaluate the sine, cosine, and tangent of the angle without using a calculator.

$$225^{\circ}$$

Evaluating Trigonometric Functions Using Technology

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In Exercises $15-22,$ write each expression as the sine,cosine$,$ or tangent of a double angle. Then find the exact value of the expression.

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2 \sin 22.5^{\circ} \cos 22.5^{\circ}

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Write each expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression.

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2 \sin 22.5^{\circ} \cos 22.5^{\circ}

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Find the exact values of the sine, cosine, and tangent of the angle.

$$255^{\circ}=300^{\circ}-45^{\circ}$$