Quiz tomorrow! Your quiz has 12 questions and 2 bonus questions. Study your notes and don't forget to bring your 1/2 sheet of notes as a reference sheet.
The examples that we did in class today will help you greatly with your quiz. If you can do those, you'll be just fine on the quiz.
Review sheets were collected today. If you didn't turn it in then I will take it tomorrow for half credit. I'm not taking any review sheets that are more than two days late.
Thursday, August 29, 2013
Wednesday, August 28, 2013
The Six Trig Functions (2 days)
The Six Trig Functions are sine, cosine, tangent, cosecant, secant, and cotangent. We can use SOHCOATOA (sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, and tangent = opposite/adjacent) to help us solve for missing sides of right triangles. It is convenient if we already have a picture of the right triangle to help us, but sometimes, this is not the case. We may often need to draw the angle ourselves on a coordinate plane. We can do this using a point and the origin or using the origin along with an equation of a line.
Important things to remember when you are drawing your graph/angles:
-Begin in standard position, at zero degrees.
-Always rotate counterclockwise, in the positive direction, unless otherwise specified by the problem.
-Your angle (theta) always goes closest to the origin
-When drawing your triangle, draw it closest to the positive side in which you are rotating.
-Solve for a missing side using the Pythagorean Theorem. We don't necessarily have to know what the angle measure is in order to do this.
-Leave your answers in radical form. I prefer "the square root of 5" as opposed to 2.236. Why? Because radical notation is, mathematically, more accurate.
Bring your review sheets tomorrow! Quiz Friday!
Important things to remember when you are drawing your graph/angles:
-Begin in standard position, at zero degrees.
-Always rotate counterclockwise, in the positive direction, unless otherwise specified by the problem.
-Your angle (theta) always goes closest to the origin
-When drawing your triangle, draw it closest to the positive side in which you are rotating.
-Solve for a missing side using the Pythagorean Theorem. We don't necessarily have to know what the angle measure is in order to do this.
-Leave your answers in radical form. I prefer "the square root of 5" as opposed to 2.236. Why? Because radical notation is, mathematically, more accurate.
Bring your review sheets tomorrow! Quiz Friday!
Monday, August 26, 2013
Coterminal Angles in Radians
Thus far, we have measured everything in degree mode. The second way to measure an angle is in radians, which is in reference to the circumference of a circle. Radians always have the term π as part of the expression.
To convert from degrees or radians, we must multiply by either (π/180) or by (180/π). Use the first one to convert to radians and the second one to convert to degrees.
Finally, we made the trig unit circle in both degrees and radians for our reference. You may use this reference sheet on a quiz or a test. The trig unit circle is the image shown below, and it shows commonly used angles in trigonometry.
To convert from degrees or radians, we must multiply by either (π/180) or by (180/π). Use the first one to convert to radians and the second one to convert to degrees.
Finally, we made the trig unit circle in both degrees and radians for our reference. You may use this reference sheet on a quiz or a test. The trig unit circle is the image shown below, and it shows commonly used angles in trigonometry.
Saturday, August 24, 2013
Coterminal Angles
Coterminal angles are those whose measures differ by a multiple of 360 degrees. An angle can have both positive and negative coterminal angles. When finding the negative coterminal angles, we must rotate backwards on the coordinate plane, so make sure to draw your angles carefully!
Similar Triangles
Similar Triangles have the same angles (all 3) but different side lengths. We can solve for the missing side of a triangle by setting up a proportion and solving for the missing side. If we have a right triangle, remember that we can also use the Pythagorean Theorem to solve for a missing side.
In complicated diagrams, it often helps to redraw the similar triangles separately so that you can align your measurements properly. Sometimes you must look carefully to spot the similar triangles!
In complicated diagrams, it often helps to redraw the similar triangles separately so that you can align your measurements properly. Sometimes you must look carefully to spot the similar triangles!
Wednesday, August 21, 2013
Geometry Review
We took a trip down memory lane and reviewed some important geometric ideas that might serve us useful this year in trig. Particularly, we looked at seven main ideas: Supplementary angles, complementary angles, congruent, vertical angles, corresponding angles, alternate interior angles, and alternate exterior angles. Then we did a few examples on what those problems could look like in the context of algebra.
Shout out to Cody Gracey for remembering most of this material from geometry, and shout out to 2nd period for being the most enthusiastic class that I've ever seen! WOW.
Shout out to Cody Gracey for remembering most of this material from geometry, and shout out to 2nd period for being the most enthusiastic class that I've ever seen! WOW.
Tuesday, August 20, 2013
Pre-Test Day
We took the pre-test today since youtube.com is an epic fail on our internet. The first review sheet was given out in class and is due back on Thursday, August 29th for full credit. If you give it to me a day early, I will give you five extra bonus points.
When grading, I give two points per question - one for the correct answer and one for shown work.
If you were absent today and missed the pre-test, you have one week from today to make it up. If it's not made up by next Tuesday it's a zero - don't let that be you!! A great time to make up work would be during my service period (3rd), during my lunch (3rd lunch) or after school.
Shout out to Bre Boyd for making me laugh and to Brasha Campbell for reading out loud even though she had a sore throat today - love the perseverance!
When grading, I give two points per question - one for the correct answer and one for shown work.
If you were absent today and missed the pre-test, you have one week from today to make it up. If it's not made up by next Tuesday it's a zero - don't let that be you!! A great time to make up work would be during my service period (3rd), during my lunch (3rd lunch) or after school.
Shout out to Bre Boyd for making me laugh and to Brasha Campbell for reading out loud even though she had a sore throat today - love the perseverance!
Monday, August 19, 2013
Welcome to Algebra 3 aka Trigonometry! I am Ms. Doc and I will be your instructor this year. We are spending a large majority of the year in discussion of the six trigonometric functions (sine, cosine, tangent, cotangent, secant, and cosecant). I promise to make it manageable and a strong learning experience for all who take part in this class.
Today we went over the syllabus and filled out a brief survey so that I could learn more about you and how you've been taught in mathematics over the past year. We also talked about where students wanted to go to college, and WHY they wanted to be there (not just to study, but really, what DRIVES you to do what you do?)
Remember to bring back your signed syllabus! +5 bonus points if I get it tomorrow (Aug 20th), regular credit if I get it by Wednesday Aug 21st. No credit if it's late.
Today we went over the syllabus and filled out a brief survey so that I could learn more about you and how you've been taught in mathematics over the past year. We also talked about where students wanted to go to college, and WHY they wanted to be there (not just to study, but really, what DRIVES you to do what you do?)
Remember to bring back your signed syllabus! +5 bonus points if I get it tomorrow (Aug 20th), regular credit if I get it by Wednesday Aug 21st. No credit if it's late.
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