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Graphing: Find the Critical Points: I will be able to graph and identify properties of sine and cosine graphs. The graph above is the image of a sine graph. I was only given the equation I had to graph it on my own in order to graph it I had to find out the period, amplitude, and the critical interval the outside number tells me that the amplitude of my graph is 3 and this is a vertical stretch not compression since it is a whole number. Also I know this is a sine graph so it will start at (0,0) not at it's amplitude like cosine. The inside number is 2, (this is my frequency). 2 pi divided by this number 2 will give me the period pi. To find the critical interval you take your period, which in this case is pi and divide it by 4. I take this number and add 1 until I get my period. These numbers will make up my x-axis numbers. Now that I have all of my information I can graph it. The graph above is what I got.  One misconception I had was I did not know I had to use the criti...

Sine and Cosine graph:                                               Sine Graph                                                   Cosine Graph The difference between sine and cosine graphs are sine graphs touch the x-axis at pi and 2 pi and one period is 2 pi, also the amplitude is pi/2. For Cosine the graph touches the x-axis at pi/2 and 5pi/3. Sine graphs start at (0,0) while Cosine graphs starts at its amplitude on the y-axis.

Transformations of sine and cosine graphs: I will be able to transform sine and cosine graphs An example of a transformation of a sine graph is y= 4cos2x. The amplitude is 4, the period is pi, with a horizontal compression by a factor of 2. The amplitude is the number in front of the trig so in this case 4. The period is found when you take the frequency which comes before the variable (x) and divide it by 2 pi. Also I know that 2 is a horizontal compression because it is inside the equation and is a whole number. One misconception I had was I thought the frequency was the same as the period until Mrs. Burton explained the difference and told us that you have to use the frequency to find the period. EQ: How do I transform the graphs of trigonometric functions? You have to find out what the amplitude, vertical and horizontal compression/stretches, period, and find out if the graph reflects or not. The amplitude is the number in front of the equation this number also tells you ...

Finding coterminal and reference angles: I will be able to find the coterminal and reference angles. One example of an Coterminal angle is: Find the coterminal angle 86 degrees. To find the angle all you need to do is add or subtract 360 degrees, 86+360= 446 degrees or 86-360 = -274 degrees One example of an Reference angle: Find the reference angle of 312 degrees.  To find the angle I would first need to find out what quadrant it falls into. 312 degrees falls into quadrant 4. 312 is close to 360 so I would just subtract 360 from 312 and get 48 degrees. Before I say this is my final answer I need to make sure it follows the 2 rules that the reference angle has, which is it has to be positive and less than 90 degrees and 48 degrees ticks both of those boxes so 48 degrees is the answer. One misconception I had was with negative degrees. I didn't know which way they would go on a circle. I figured out my misconception when Mrs. Burton clarified it to the class that negative d...

Evaluating and Converting: I will be able to evaluate trigonometric expressions and convert between radians and degrees. One example of evaluating is: Find Cot 45 degrees. Cot is the inverse of tangent so 1/tan(45)= 1 One example of converting radians to degrees: Convert 3pi/4 into degrees. First I would need to multiply 3pi/4 by 180/pi. The pi's would cancel and I would end up with 3*180/4 ---> 135 degrees is the answer. One example of converting degrees to radians: Convert 160 degrees in radians.  First I would multiply 160 by pi/180. 160 pi/180. This is no the simplified form so I would need to divide the top and the bottom by 20 and the final answer is 8pi/9 One misconception I had was with which equation to use to convert from radians to degrees or degrees to radians. I figured out my misconception on my own I figured the pi would be in the numerator when going from degree to radian because radians have pi and the pi would be in the denominator when going from r...

Trigonometric Word Problems: I will be able to find trigonometric ratios of acute angles. One example of a trigonometric word problem is: A 15 foot ladder rests against a tree on level ground and forms a 75 degree angle of elevation. What is the height of the tree? What is the distance of the tree to the base of the ladder. The first step in solving this problem would be to go through and find any important information. I know that the ladder leaning against the tree forms a right angle so I will be using a trig ratio. The ladder is 15 feet long and is the hypotenuse so I have one length. The ground under the tree forms a 75 degree angle of elevation. This angle is across from the 90 degree angle. To solve this problem I need to find height and the base of the tree from the ladder. To find height I need to find the Sine (opposite over hypotenuse) 75 degrees = x/15. If I multiply 15 to both sides I can cross out the 15 in the denominator: 15(sin75)=x, x is approximately 14.49...

Exponential Word Problems I will be able to use compound interest to solve exponential problems. One example of an Exponential word problem is: Find the accumulated amount of money after 5 years if $4,300 is invested at 6% per year compounded quarterly . Find the growth factor .  In order to solve this problem you have to find out the accumulated amount after (t) number of years, which in this problem is what we are supposed to find out, the principle (original amount) which is 4300 (P) , the nominal interest rate per year, which is 6% or .06 (r) , the number of periods or years (n) , which is 4 because the money is compounded quarterly which is 4 times a year, and the number of years (t) , which is 5. Then you plug these numbers into the compound interest formula. A=P(1+r/n)^n*t ------->  A=4300(1+.06/4)^4*5 --------->  A=5791.48 The accumulated amount after 5 years is approximately $5791.48. The growth factor is 1.015 One misconception I had...