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$\cdot$ An angle is given, to one significant figure, as $4^{\circ},$ meaning that its value is between $3.5^{\circ}$ and $4.5^{\circ} .$ Find the corresponding range of possible values of $(a)$ the cosine of the angle, (b) the sine of the angle, and (c) the tangent of the angle.

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a) $ \sin \left(3.5^{\circ}\right) =0.0610 $$ \sin \left(4^{\circ}\right) =0.0698 $$ \sin \left(4.5^{\circ}\right) =0.0785 $Hence when using the $\sin \left(4^{\circ}\right),$ our values are ranging from 0.061 to 0.0785b) $\cos \left(3.5^{\circ}\right)=0.9981$$\cos \left(4^{\circ}\right)=0.9976$$\cos \left(4.5^{\circ}\right)=0.9969$Hence when using the cos( $\left(4^{\circ}\right),$ our values are ranging from 0.9981 to 0.9969c) $\tan \left(3.5^{\circ}\right)=0.0612$$\sin \left(4^{\circ}\right)=0.0699$$\sin \left(4.5^{\circ}\right)=0.0787$Hence when using the $\tan \left(4^{\circ}\right),$ our values are ranging from 0.0612 to 0.0787

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to be in chapter on problems of you. And so this says that angle is given toe once a figure such as or degrees. But this means this value could actually be between 3.5 degrees and 4.5 degrees. So we want to find the course on the range of possible values for the coast on Diego, the sine of the angle and attention. So, first for the coastline to do this, we find a co sign value at each the lower value tell you in the back so co sign of 3.5 ovaries equals zero part nine now a one in a co sign of 4.5 series. Because zero reporting 9 96 not a 10. So that was a range as on the brains of zero point 9969 to 0 point nine. No, Eh, good. We want to be now we do it in sign functions. So screwed a sign of report of five and this is 0.61 in sign of 4.5. This turned out to be 0.78 So our range is 0.6120078 Last Let's do with the tendon function. Tangent of 3.5 degrees is 0.61 and tangent of 4.5 degrees. Zero for zero, said nine Mate. That's actually nine. So our range is very similar to the sign here, she reported. 6120.79 Awesome.

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