Sunday, October 7, 2012
Practice with degrees and radians.
Here is a link to a blog post explaining degrees and radians with some practice problems.
Here are more practice problems for writing angles both in degrees and radians, where the degrees number is between 0° and 360° and the radians number is between 0 and 2pi.
This text editor can't write the superscript -1, so I'll use the "arc" prefix to discuss the inverse trig functions.
arccos(-.25): In degrees mode, the answer is 104.4775122...°, which I would round to 104.4775°. Changing to radians mode, the answer is 1.823476582..., which I would round to 1.8235 radians.
Dividing that answer by pi, I get .580430623..., which I would round to .5804pi.
arcsin(-.25): In degrees mode, the answer is -14.47751219...°. Adding 360° and rounding, the answer is 345.5225°.
Instead of changing to radians mode, I could just divide this by 180 to get 1.919569377... which is to say the reading rounds 1.9196pi radians.
Multiplying by pi, I get 6.030505052..., or 6.0305 radians.
Practice
a) arctan(-.25)
b) arccos(1/12)
c) arcsin(-1/12)
Answers in the comments.
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ReplyDeletea) arctan(-.25)
In degree mode we get -14.03624347...°, so we add 360° and round to get 345.9638°.
Dividing by 180, the answer is 1.92202087, which rounds to 1.9220pi radians.
Multiplying by pi, the answer is 6.0382 radians.
b) arccos(1/12)
In degree mode we get 85.21980815...°, so round to get 85.2198°.
Dividing by 180, the answer is 0.473443379..., which rounds to 0.4734pi radians.
Multiplying by pi, the answer is 1.4874 radians.
c) arcsin(-1/12)
In degree mode we get -4.780191847...°, so we add 360° and round to get 355.2198°.
Dividing by 180, the answer is 1.973443379..., which rounds to 1.9734pi radians.
Multiplying by pi, the answer is 6.1998 radians.