trig
- Thread starter swimmer3
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More than one option.
(1) Get out your calculator and enter each and compare results.
(2) Draw a sketch of each on the unit circle. Compare the lengths of the corresponding abscissas.
(3) Just do some thinking. You know the value of cos 0°. You should know the value of cos 45°. Determine how the value of the cosine function changes as it goes from 0° to 45°. Realize that cos 35° is trapped between.
Possibly others will give you other suggestions.
(1) Get out your calculator and enter each and compare results.
(2) Draw a sketch of each on the unit circle. Compare the lengths of the corresponding abscissas.
(3) Just do some thinking. You know the value of cos 0°. You should know the value of cos 45°. Determine how the value of the cosine function changes as it goes from 0° to 45°. Realize that cos 35° is trapped between.
Possibly others will give you other suggestions.
mmm4444bot
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- Oct 6, 2005
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If you've learned about right-triangle trigonometry, then a quick sketch and some reasoning about ratios is sufficient.
Fix the base of both triangles at 1 unit.
Do you see how the terminal side of the angle (i.e., the hypotenuse) gets longer as the angle measure increases?
The hypotenuse L is Longer, and the hypotenuse S is Shorter, but the adjacent side is the same for both.
Cosine is the ratio: Adjacent/Hypotenuse.
The ratio 1/S is larger than the ratio 1/L because a fraction with a fixed numerator GROWS as the denominator gets smaller.
However, I like Loren's unit-circle approach better because I can quickly see in my mind that the x-coordinate (i.e., the cosine) gets smaller as the angle increases in Quadrant I.
This is analagous to thinking about the shape of the graph of y = cos(x); as the angle (which is x) goes from 0 to Pi/2, the angle's cosine (which is y) goes from 1 to 0.
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