Tan, Cos, and Sin... To the nearest degree.

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Masonan

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I can't quite figure out what my textbook is asking of me. I have a chart that compares degrees with their cos, sin, and tan values. The questions include the phrase: "to the nearest degree". I'm not sure what they mean by this. For instance

1) Find angle 'B' with hypotenuse '9' and opposite '3' to the nearest degree.

The equation works out like this:

sin=3/9=1/3
sin=.3333

I can see one possible answer for this:

A) 19 degrees = .3256 (.3333 - .3256 = 77)
B) 20 degrees = .3420 (.3420 - .3333 = 87)

Obviously since the sine of '19 degrees' is both before the actual sine of this answer on the sin chart and is actually the closest, it is the correct answers.

This is where I'm confused

2) Find the value of Angle A where the adjacent side = 10 and the opposite side = 5

The equation works out like this:

Tan = 5/10 = 1/2
Tan = .5000

Which answer would be correct?

A) 27 degrees = Tan .5095 (.5095 - .5000 = 95)
B) 26 degrees = Tan .4877 (.5000 = .4877 = 123)

A is technically the closest in difference, but B is the closest without going over the number. Which one is correct? The book doesn't explain this.

3) Cos _____ = 0.96 to the nearest degree
16 degrees or 17 degrees? Same issue

Thanks for the help. You guys are great.
 
I don't know how to use a scientific calculator to check my answer. Any explanation?
 
Masonan said:
I can't quite figure out what my textbook is asking of me ... "to the nearest degree". I'm not sure what they mean by this.
Click to expand...

This instruction is asking you to round to the nearest degree. But the rounding is taking place with the ratios, instead of with the actual angle value.

Unless you have information to the contrary, it matters not whether the round-off error on the trigonometric ratio is an "overage" or an "underage". You round by going with the angle that yields the closest trigonometric value to the determined goal, regardless of whether this value is larger or smaller than the determined ratio.

For example, when trying to choose between 26º and 27º for the nearest angle with a tangent of 1/2, choose 27º because the round-off error is less than it is for 26º, as you calculated.

The actual angle in degrees whose tangent is exactly 1/2 (to five decimal digits of precision) is 26.56505º

This is closer to 27º than 26º.

Cheers,

~ Mark :)
 
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