ShmoopTube
Where Monty Python meets your 10th grade teacher.
Search Thousands of Shmoop Videos
Cosines 1275 Views
Share It!
Description:
It's the sine! No, it's the tangent! No, it's the cosine! Alright, so maybe evaluating trigonometric functions isn't as exciting as spotting Superman in the sky. But we bet you jump for joy the first time you solve for cosine.
Transcript
- 00:04
Cosines, a la Shmoop.
- 00:06
Daniel and Mary are both excited to move in and start their new lives together.
- 00:10
However, Daniel's mother has decided to come along for the ride.
- 00:15
She promises to stay out of their way. She just has one request.
- 00:18
The walls must be hot pink.
Full Transcript
- 00:21
Daniel and Mary need to figure out how long their ceiling is before they buy the paint.
- 00:26
They know the angle between the edge of the house and the floor is 22 degrees...
- 00:30
...and that the distance from one corner to the center of the room is 14 feet.
- 00:36
What is the length of the ceiling?
- 00:39
We can call our variable, the length of the ceiling, L.
- 00:43
To find L, we can use the cosine ratio.
- 00:46
The cosine of an angle is the adjacent side of the angle over the hypotenuse.
- 00:51
Plugging in what we know, cosine of 22 degrees
- 00:54
equals the adjacent side length, 14, over the hypotenuse or L
- 00:59
To isolate L, we can multiply both sides by L to get it out of the denominator.
- 01:05
Then, we divide both sides of the equation by cosine 22 degrees...
- 01:09
...to find that L equals 14 over cosine 22,
- 01:13
We can look up the cosine of 22 degrees in a handy dandy table like this...
- 01:17
...or if you have a calculator with a cosine function...
- 01:20
...just hit the cosine button followed by 22 and then enter to get approximately 15.1 feet.
- 01:28
Just to be sure, though, they decide to figure out the cosines of a few more angles...
- 01:33
...in case they ever move and have to do this again.
- 01:35
They decide to try the angles: 0 degrees, 30 degrees, 45 degrees, 60 degrees, and 90 degrees.
- 01:42
Doing some calculations, they learn that:
- 01:45
The cosine of 0 degrees is 1.
- 01:48
The cosine of 30 degrees is the square root of three over two, or .866.
- 01:55
The cosine of 45 degrees is one over the square root of two, or .707.
- 02:01
The cosine of 60 degrees is a half, or 0.5.
- 02:05
The cosine of 90 degrees is zero.
- 02:09
Mommy dearest gets her hot pink walls.
- 02:11
Daniel and Mary are happy now as well, for the most part...
- 02:15
...aside from all the unexplainable headaches...
Up Next
Verifying trig identities is important, especially when you're about to let one of them into the country—which is why they should keep their pass...
Related Videos
Mosquitos need their caffeine, just like the rest of us. Wouldn't think zipping around and stinging people all day long sap your energy?
Sine is the opposite over the hypotenuse; cosine is the adjacent over the hypotenuse; and tangent is the opposite side over the adjacent side....
Shmoop saw the sine. Want to pull an Oliver Twist and ask us for more? We've gotcha covered. Head over to /video/math/ for more mathy goodness. No...
ACT Math Trigonometry Drill 1, Problem 2. Can you find the tangent?