Thread: Help w/ Trig Questions

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

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

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.

i put 9640km its wrong

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.

i dont understand this question

Originally Posted by rock candy

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

$\displaystyle 360^\circ$ corresponds to $\displaystyle 2\pi$ radians (because a circle has a circumference of $\displaystyle 2\pi r,$ or $\displaystyle 2\pi$ radii).

So, to convert between radians and degrees, use the conversion

$\displaystyle 360^\circ=2\pi\text{ rad}$

or

$\displaystyle 180^\circ=\pi\text{ rad}\text.$

Also, pie is something you eat. The ratio of the circumference of a circle to its diameter is denoted by the Greek letter pi.

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

Learn your unit circle. You should be able to evaluate $\displaystyle \sin\frac\pi3$ and $\displaystyle \cos\frac\pi3\text.$ This expression is simple enough to evaluate without a calculator; you should get $\displaystyle \frac54\text.$

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.

i put 9640km its wrong

You should have posted your work on the problem. That way, we could have pointed out your error more easily.

Based on your answer, I am guessing that you used the wrong radius. $\displaystyle 6400\text{ km}$ is the radius of the Earth, not the radius of the satellite's orbit (otherwise the satellite would be dragging itself along the ground!). Fix your radius and you should get the correct result.

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.

$\displaystyle 8-\tan\theta = 0\Rightarrow\tan\theta=8\text.$

Use the inverse tangent function to get the quadrant I angle. The tangent function is also positive in quadrant III, so there is a solution there as well.

By itself, the equation has infinitely many solutions, but we are only interested in those for which $\displaystyle 0\leq\theta<360^\circ$ ("nonnegative" means positive or zero).