[SOLVED] Radians/degrees conversions, want confirmation of answers

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February 22nd 2009, 07:22 AM
rock candy

[SOLVED] Radians/degrees conversions, want confirmation of answers

k well ... i did the following

1. Convert the angle given in degrees to radian measure in terms of pi.
380*
Round the coefficient to two decimal places

well i converted 380* in terms of pi
and i got : 19/9 pi ( its wrong)

2. Evaluate to four significant digits.
sin^2 pi/3 + cos pi/3

sin^2 pi/3 + cos pi/3
and i got : 1.019 ( and this is wrong as well)

3. A satellite is in a circular orbit 225 km above the equator of the earth. How many kilometres must it travel for its longitude to change by 86.3°? Assume the radius of the earth equals 6400 kilometres.
Round the answer to the whole.

86.3* x pi/180* = 1.506 rad theta = s / r

1.506 rad x 225 km = s
338.89 = s ( rounded to the nearest whole number)
340 = s ?

4. Solve the equation 8- tan theta = 0 for all nonnegative values of theta less than 360* . Do by calculator, if needed, and give the answers to three significant digits in the order of increasing.

inverse tan (8) = angle
theta = 82.9 (3 sig figs)
theta = 263 (3 sig figs)
February 22nd 2009, 07:36 AM
Air

Quote:

Originally Posted by rock candy

k well ... i did the following

1. Convert the angle given in degrees to radian measure in terms of pi.
380*
Round the coefficient to two decimal places

well i converted 380* in terms of pi
and i got : 19/9 pi ( its wrong)

No, this is correct. To convert from degree to radian you multiply the theta (in degree) value by $\frac{\pi}{180}$ .

$\therefore 380 \times \frac{\pi}{180} = \frac{19\pi}{9} \approx 6.63 \ {\mathrm{Radians}}$

Quote:

Originally Posted by rock candy

2. Evaluate to four significant digits.
sin^2 pi/3 + cos pi/3

sin^2 pi/3 + cos pi/3
and i got : 1.019 ( and this is wrong as well)

You have an arithmetic error.

$\sin \left(\frac{\pi}{3} \right) = \frac{\sqrt{3}}{2} \therefore \sin ^2 \left(\frac{\pi}{3} \right) = \left(\frac{\sqrt{3}}{2}\right)^2 = \frac34$

$\cos \left(\frac{\pi}{3} \right) = \frac12$

Quote:

Originally Posted by rock candy

3. A satellite is in a circular orbit 225 km above the equator of the earth. How many kilometres must it travel for its longitude to change by 86.3°? Assume the radius of the earth equals 6400 kilometres.
Round the answer to the whole.

86.3* x pi/180* = 1.506 rad theta = s / r

1.506 rad x 225 km = s
338.89 = s ( rounded to the nearest whole number)
340 = s ?

The total distance (radius to be used) is the radius of the earth plus distance to the satelite.

$\therefore r = 6400 + 225 = 6625 \ \mathrm{km}$

Quote:

Originally Posted by rock candy

4. Solve the equation 8- tan theta = 0 for all nonnegative values of theta less than 360* . Do by calculator, if needed, and give the answers to three significant digits in the order of increasing.

inverse tan (8) = angle
theta = 82.9 (3 sig figs)
theta = 263 (3 sig figs)

This is correct. (Clapping)
February 22nd 2009, 09:18 AM
rock candy

k i got 1 and 4 right ..

2 i got wrong .. the answer was this

http://edugen.wiley.com/edugen/share...=1235308545638
answer is 1.25

3. i added the 2 radius to get the total like you and used theta = s / r ... and i got 9980 km ... :S and its wrong
March 6th 2009, 05:05 PM
Jhevon

Quote:

Originally Posted by rock candy

2 i got wrong .. the answer was this

http://edugen.wiley.com/edugen/share...=1235308545638
answer is 1.25

an error in regards to this problem was made in the previous post, it has been fixed. check again

Quote:

3. i added the 2 radius to get the total like you and used theta = s / r ... and i got 9980 km ... :S and its wrong

you rounded up too much. it should be 9979