Mr. Markwalter Start new unit Return projects/tests Oh? So you’re starting a new unit? Three is the bee’s knees. We have seen sine and cosine graphs Now, we will look at our other 4 functions Why? We have seen sine and cosine graphs Now, we will look at our other 4 functions Why? To get ready for solving bigger trig problems. For example… The hot-air balloon festival held each year in Phoenix, Arizona, is a popular event for photographers. Jo Silver, an award-winning photographer at the event, watches a balloon rising from ground level from a point 500 feet away on level ground. Write the angle of elevation as a function of the height of the balloon. We need to get a grasp of our other functions (not as long a unit as last time). The graphs we have seen of sine and cosine functions have some similarities. Let’s name some. A lot of these are obvious from the graphs. Let’s see some. Now, if I wanted to make sin(x) become cos(x), what would I need to do to the graph? Shift it to the left. How much? π/2 And how would we do that? cos(x)=sin(x+π/2) Sine and cosine can be interchanged! How would we get cos(x) to be sin(x)? sin(x)=cos(x-π/2) Write the following cosine function as a sine function. f(x)=3cos(x)-2 Write the following cosine function as a sine function. f(x)=3cos(x)-2 To go from cos(x) to sin(x), add π/2 inside the argument. g(x)=3sin(x+ π/2)-2 Write the following sine function as a cosine function. f(x)=-2sin(x)+1 Write the following sine function as a cosine function. f(x)=-2sin(x)+1 To go from sin(x) to cos(x), subtract π/2 inside the argument. g(x)=-2cos(x- π/2 )+1 Come get a whiteboard and a marker. Nice a calm! Copy down the problem in your notebook. Solve it there. Put your answer on your board. This can be a resource for going back for your THIRD encounter. Given the function, rewrite it as an equivalent sine or cosine function. What we are doing is REALLY shifting the graph a QUARTER OF A PERIOD. You need to first figure out the period! Then adjust our function! Write h(x)=3cos(2πx) as a sine function. Write h(x)=3cos(2πx) as a sine function. Find the period. Add one fourth of it. Write h(x)=sin(π/2 x)-4 as a cosine function. Find the period. Subtract one fourth of it. Write h(x)=-2cos(π/4x)+2 as a sine function. Find the period. Find ¼ of the period. Add or subtract it appropriately. Don’t forget the parentheses! Take in out and let’s practice! In general, looked ok. I put a score out of 16 on your rubric. Everyone got the same score UNLESS I noted something differently on the evaluation YOU handed in. Your personal grade is in the gradebook. If you have questions, find me. 1st period average: 68.6% 3rd period average: 69.1% 6th period average: 64.7% Now, clearly there is room for improvement. Changes to make ups. ◦ Correct your test. ◦ Write one problem for each you missed and solve it. ◦ Make-up days: this Thursday, next Tuesday, next Thursday I will hand back projects to ONE person in the group. Tests are filed in the folders. Complete the worksheet for homework.