1. |
Explain the term coterminal. |
2. |
What are complementary angles? |
3. |
What are supplementary angles? |
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In the following problems, find the sum
and the difference
of the two given angles.
4. |
![{\displaystyle A=38^{\circ }15^{\prime }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bac6e1d006dc2776672ef870056c3be0dc9eaf8b) |
![{\displaystyle B=17^{\circ }5^{\prime }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5356d26b9273c83577b1ba7b8d0f41a1d2dec772) |
5. |
![{\displaystyle A=98^{\circ }41^{\prime }42^{\prime \prime }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3fb4a2e5f26a0fb853a033b3b8d261a11a9701ec) |
![{\displaystyle B=50^{\circ }25^{\prime }55^{\prime \prime }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/75a450d4e698a6ad4d9301a9223a2fe7941fab93) |
6. |
![{\displaystyle A=150^{\circ }2^{\prime }1^{\prime \prime }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/36c06be240c6e6b80a75b154f52539cf2bc91060) |
![{\displaystyle B=266^{\circ }44^{\prime }9^{\prime \prime }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/457ece4854e60c7e7dad0ad8bd03461fb266a20e) |
7. |
![{\displaystyle A=-18^{\circ }11^{\prime }19^{\prime \prime }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ef31912bf1faf7c0cafb2b52f5f4a5c7ef4e821e) |
![{\displaystyle B=38^{\circ }17^{\prime }17^{\prime \prime }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4ebb9a27cc882deee7d19c7d62926d77098cb0ee) |
8. |
![{\displaystyle A=138.7222^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a16417d9757bab6a335168ce04494730bbfe5b38) |
![{\displaystyle B=21.9111^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ec55e4925b39701f3f02ae3ab6bfcc26eb9f8a58) |
9. |
![{\displaystyle A=335.8500^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/efa65ee2f0b0713e35014753b268d79e19376ba5) |
![{\displaystyle B=-34.9500^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/24ad3d077556fceef80526849a71da099e44805c) |
10. |
![{\displaystyle A=-48.8^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9b58e503b9209a76a52e1050ab6f134fc6364b39) |
![{\displaystyle B=336.4556^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/662f3d3f06ad199f378b9fd641d852c1e1b552ad) |
11. |
![{\displaystyle A=-17.6056^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f0570941d52b97ef5a1b2e4c3cee2b20ff54ae40) |
![{\displaystyle B=-87.2694^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5b922231bfad0ae632e1369ddc8c1c7f33f5a3ba) |
| | |
In the following problems convert the given angle in degrees, minutes, seconds to decimal degrees.
12. |
![{\displaystyle 38^{\circ }15^{\prime }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c1c0518178c999d04fb7fd3a21129c8e465036d0) |
13. |
![{\displaystyle -71^{\circ }22^{\prime }43^{\prime \prime }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ea7c2861ced9551efc280f74be057cc6df0cdbcc) |
14. |
![{\displaystyle 428^{\circ }0^{\prime }18^{\prime \prime }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/66abb31d53f589210250ca9cc583fcb2ce8bb909) |
15. |
![{\displaystyle 180^{\circ }17^{\prime }38^{\prime \prime }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bd98a4568a3c0c4d06a69c28c4c5deb7c1563e79) |
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In the following problems convert the given angle in decimal degrees to an angle in degrees, minutes, seconds.
16. |
![{\displaystyle 279.6938^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ebcbda8a92d28c2de62efae144885c80310256f2) |
17. |
![{\displaystyle -23.3040^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ee199c40d39d6e4c095c8b95d99a743bf2a29afe) |
18. |
![{\displaystyle 167.0030^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/702989e39e0d95afdab1b8f304183a17402b68e4) |
19. |
![{\displaystyle 316.2575^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/18c29ce688df8ba80084510067d87f9ff842489a) |
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Example: The point (5,6) is plotted and the line is measured to be about fifty degrees with the x-axis.
On paper, draw the following angle. If the angle is negative or larger than
, convert it to an angle between
and
.
20. |
![{\displaystyle 72^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0cfa1907f003a92fb16d6a32aa7a4f5da99f112) |
21. |
![{\displaystyle 400^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c7c0d78e85f3fe19dd2b8a03bbfea666d76ed1cf) |
22. |
![{\displaystyle -42^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5399d65446d73f06d674e1af884d80cd7bc09e24) |
23. |
![{\displaystyle -395^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4335f2b12a3827a0ef076a27b38adc8d73564eef) |
| |
On graph paper plot the following points and measure the angle with a protractor.
24. |
![{\displaystyle \left(7,2\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/34802168803c976da3b5c311e65b117d9cc6b08a) |
25. |
![{\displaystyle \left(-5,7\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4c5a63805628618ba1dd7d4851cc73ea236a631a) |
26. |
![{\displaystyle \left(-2,-8\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/018e3ced22f0cd28f76bd2da8d093ad088ce95f6) |
27. |
![{\displaystyle \left(1,-5\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/60f7936077046865f6bf3fd719e90be5134f4f37) |
| |
28. |
During an orienteering competition, you are headed in a compass direction of . |
|
You find that you need to head in the direction of . |
|
How far must you change your course in order to travel in the new direction. |
29. |
Tuning the engine of your early model Chevy Camaro, you find the sparkplug fires at ![{\displaystyle 1^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/01e25bbf2306d1eb8d32184a2f1b4477bf3b201b) |
|
after the flywheel reaches the top position. You want the sparkplug to fire at ![{\displaystyle 5^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8e36cd1f9d42eec7d74270a62863a7e7f4f356c7) |
|
before it reaches the top. How many degrees must you adjust the timing so that it fires correctly? |
30. |
If your bicycle wheel spins around twice, how many degrees has it rotated? |
31. |
A radar antenna rotates twice each minute. How many degrees will it rotate in an hour and a half? |
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