Greetings everyone,
How was class today? I'm sure that all of you worked hard in your groups and helped one another. If you have any questions, feel free to post a comment. I will be online until around 10 pm to help you. Be sure to read the notes I left on the board regarding pacing yourself on the test. If you know the objectives and how to work all types of problems you will do fine. You have 45 minutes for part I (no calc.) and 45 minutes for part II (Calculator, 9 application problems).
Part I is the basics: simple stuff like graphs of sinusoids, coterminal angles, and inverse trig function problems like arcsin (sin PI). On part II, you may see a bearing problem and a harmonic motion problem in addition to the "basic" triangle trig word problems.
Good Luck! I'd love to hear from you:)
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6 comments:
Hey Mrs. Snipes!
So I was working on the assignment you left for us today, and I am still having trouble with angular and linear velocities. I was wondering if you could help me out with this problem : A truck is moving at a rate of 90 kilometers per hour, and the diameter of its wheels is 1 meter. Find the angular speed of the wheels in radians per minute.
Thanks!
I don't understand how set up the bearings problems like pg.212 #18. I also don't understand #8. I usually understand these but I can't get this one.
Also, on the study guides, I can set the problem, but I get confused on what angle to measure.
Hi Tiffany,
I did not bring my trig book with me to Montgomery, so post a comment in which you copy the problems you need help with.
Thanks
Mrs. S
18. A plane is 80 miles north and 95 miles east of Cleveland Hopkins International Airport. What bearing should be taken to fly directly to the airport?
8. Use a calculator to approximate two values of (theta) in radians (0to 2pi) if csc theta=1.030. Round the sresult to two decimal places.
5. (from the study guides) An 8m pole is leaning against a tree. The foot of the pole is 5m from the foot of the tree. What angle does the pole make with the tree? I set the numbers in the right places, but I use the wrong trig. function to solve it.
I don't have a calculator with me, but here is how to set up each problem: Good luck tomorrow :)
18. A plane is 80 miles north and 95 miles east of Cleveland Hopkins International Airport. What bearing should be taken to fly directly to the airport?
Solution: Beginning at the orgin, which represents the airport, sketch a line going north for 80 miles. Turn East (making a right angle) and travel 95 miles more.
After going east for 95 miles, sketch the hypotenuse back to the origin. The angle between the hypotenuse and the horizontal 95 mile distance is your bearing back to the airport. You can find the value of this angle by saying
tan(theta) = 80/95
2nd tan (80/95) = theta
8. Use a calculator to approximate two values of (theta) in radians (0to 2pi) if csc theta=1.030. Round the sresult to two decimal places.
Solution: sin theta = 1/1.030
Since sin theta = a positive value, theta terminates in either quadrant I or quadrant II.
Quad I angle:
Theta = 2nd sin (1/1.030)
To find your Quad II angle, subtract your quad I angle from pi. This gives you the quad II angle.
Why does this work? The quad I angle is the reference angle for the Quad II angle.
5. (from the study guides) An 8m pole is leaning against a tree. The foot of the pole is 5m from the foot of the tree. What angle does the pole make with the tree?
Solution: Theta is the angle at the top of the triangle between the vertical tree and the leaning pole. The leaning pole is the hypotenuse of the triangle.
sin theta = 5m/8m
Theta = 2nd sin(5/8)
Now, find theta on your calculator. Your calculator should be in degrees for "real life applications" such as problem 8 and 5.
November 6, 2008 8:51 PM
Hi Lauren, This is the corrected solution for your problem.
*linear velocity/radius = angular velocity.
*If we divide
(r theta)/t by r, we get theta/t which is angular velocity.
SOLUTION:
90km/hr times 1000m/1km times 1hr/60min divided by .5m/1radian
= 90000m/1hr times 1hr/60min times
1radian/.5m
=3000m/2min. times 1rad/.5
=3000rad/min.
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