If you missed class today, here are a few examples on how to graph different types of trig functions, as shown in class. Please click on the video links below for a tutorial on how to graph. Happy studying!
How to graph a horizontal translation: y = sec(x - pi/4)
How to graph a vertical translation: y = cosx + 2
How to graph a change in amplitude: y = 3cscx
How to graph a change in Period: y = tan2x
Monday, December 16, 2013
Saturday, December 14, 2013
Review Week for the Semester Exam (12/11 through 12/17)
Hello trig students! Here is what we are reviewing for the trig exam next week:
Wed 12/11: Triangles Review (Pythagorean, SOHCAHTOA, LoS, LoC)
Thurs 12/12: Six Trig Functions Review (point, line, unit circle, quadrantal)
Fri 12/13: Reciprocals and Word Problems with Triangles
Mon 12/16: Graphing Trig Functions
Tues 12/17: Arcs/Sectors (6th Period Only, I will not have 2nd or 4th today)
Wed 12/18: Wrap-up, any last minute questions, turn in review sheets
Instead of posting review information again, scroll through this blog and find examples and notes of problems that you may have forgotten how to do. There are a few videos that might be able to help you out. Finally, if you need additional assistance, COME ASK ME during a time that we both are free! Good luck and happy studying!
Wed 12/11: Triangles Review (Pythagorean, SOHCAHTOA, LoS, LoC)
Thurs 12/12: Six Trig Functions Review (point, line, unit circle, quadrantal)
Fri 12/13: Reciprocals and Word Problems with Triangles
Mon 12/16: Graphing Trig Functions
Tues 12/17: Arcs/Sectors (6th Period Only, I will not have 2nd or 4th today)
Wed 12/18: Wrap-up, any last minute questions, turn in review sheets
Instead of posting review information again, scroll through this blog and find examples and notes of problems that you may have forgotten how to do. There are a few videos that might be able to help you out. Finally, if you need additional assistance, COME ASK ME during a time that we both are free! Good luck and happy studying!
Triangles Review: Which Triangle Rule to Use?
We have four different rules for triangles - how do we know which one to use? The information below may be helpful...
First, determine if your triangle is a right triangle or not. If you have a right triangle, you can use the Pythagorean Theorem or SOHCAHTOA. Use Pythagorean if you have two sides and are missing a third side. Use SOHCAHTOA if you have an angle measure and a side.
If you don't have a right triangle, you can use either the law of sines or law of cosines. If you have angle-side-angle, use the law of sines. If you have side-angle-side or side-side-side, use the law of cosines (for the angle, make sure you leave the variable next to cosine).
If you have side-side-angle, then the triangle cannot be solved, so don't use any triangle rules!
First, determine if your triangle is a right triangle or not. If you have a right triangle, you can use the Pythagorean Theorem or SOHCAHTOA. Use Pythagorean if you have two sides and are missing a third side. Use SOHCAHTOA if you have an angle measure and a side.
If you don't have a right triangle, you can use either the law of sines or law of cosines. If you have angle-side-angle, use the law of sines. If you have side-angle-side or side-side-side, use the law of cosines (for the angle, make sure you leave the variable next to cosine).
If you have side-side-angle, then the triangle cannot be solved, so don't use any triangle rules!
Law of Cosines
The law of cosines can be used in two circumstances. First, we can use it to find the missing side of a non-right triangle when we are given a side, an angle in the middle, and another side. Or, we can use it to find a missing angle of a triangle when we are given all three sides of a non-right triangle.
The law of cosines is:
c^2 = a^2 + b^2 - 2abcos(c) where a and b are the two shorter sides of the triangle, c is the longest side, and cos(c) is either the given angle or the missing angle (if you have all three sides).
It does not matter what side you label a or b, just make sure that c is your longest side!
The law of cosines is:
c^2 = a^2 + b^2 - 2abcos(c) where a and b are the two shorter sides of the triangle, c is the longest side, and cos(c) is either the given angle or the missing angle (if you have all three sides).
It does not matter what side you label a or b, just make sure that c is your longest side!
Tuesday, December 3, 2013
Law of Sines in Real World Context
Today we practiced problems using the Law of Sines in real-life situations. In this case, we're not going to be given the triangle, we have to read the problem carefully and figure out where the correct angles and sides go. Also, remember from today, we discussed that when we make a triangle it is very important that:
<A is across from a
<B is across from b
<C is across from c
Otherwise, you're not going to set up the correct proportion (and thus, not get the right answer).
<A is across from a
<B is across from b
<C is across from c
Otherwise, you're not going to set up the correct proportion (and thus, not get the right answer).
Monday, December 2, 2013
Law of Sines
We can use the Pythagorean theorem or SOHCAHTOA to solve for missing sides and angles of RIGHT triangles. What happens when we don't have a right triangle? We use the law of sines! The law of sines says that a/sinA = b/sinB = c/sinC. We typically only use one proportion at a time.
To use the law of sines, you must be given two angles and a side. Two sides and an angle doesn't work. First, find the third missing angle by subtracting your two given angles from 180, because there are 180 degrees in every triangle. Then, use the law of sines to create proportions to solve for your missing sides!
To see a video example of how to do this, click the link below:
http://www.educreations.com/lesson/view/law-of-sines/14387213/?s=9doa0j&ref=app
To use the law of sines, you must be given two angles and a side. Two sides and an angle doesn't work. First, find the third missing angle by subtracting your two given angles from 180, because there are 180 degrees in every triangle. Then, use the law of sines to create proportions to solve for your missing sides!
To see a video example of how to do this, click the link below:
http://www.educreations.com/lesson/view/law-of-sines/14387213/?s=9doa0j&ref=app
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