Today we started with a homework quiz.
Then we proved why

We used Pythagorean theorem for the right triangle:

and we got that:
Then we used Pythagorean theorem for the left triangle:

also we used to get
Then we substituted everything from the left triangle in the equation we got for the right triangle. So the final equation is:
It works with SSS and SAS.

The next part of the unit were vectors.
In math the vector is a segment with direction, also called directed line segment:
The first point of the segment is called initial point (A), and the last point is called terminal point (B). a, b are components of the vector -
The length is sometimes referred to as magnitude,
Using Pythagorean theorem we could write it as:
The angle of the vector, θ is called direction angle.

examples:
1)Find the component form for a vector with initial point (-2,4) and terminal point (3,1).
The answer is <5,>

2)Find the component form for and θ=45º
, so
, so
The answer is

The rest of the class we went over hw.

Homework for 4/29

Some of us didn't understand problems 41 and 43 from the previous hw. Could you please post them here? Thanks.
Petra

scribe post, petra, trigonometry

We started the class with a warm-up quiz on quizlet. Then we worked on a few problems: example:
We went over hw problems we didn't know.
83)a which is so the answers are:
19) 0"> from the function value we get that
We decided that it's in the IV quadrant. We calculated hypotenuse using Pythagorean theorem. The answer is:




27) 2x-y=0, quadrant III we made a slope -> y=2x and found the sides of the triangle. Then using the sides of the triangle found all six trigonometric functions.
Then we went on the site for a Ferris Wheel. http://maine.edc.org/file.php/1/AssessmentResources/FerrisWheelUnitCircle32_L.html
We tried to make a graph where height was on y-axis and time on x-axis.
Then we used a function
We found it's domain: all real numbers
and range: [-1, 1]
Then we made a graph where f (θ) was on y axis and θ was on x axis.
We then used GeoGebra and made a graph for g(θ) = cos (θ), where we used different values for θ in radians.
At the end we used a function:
to define amplitude of sine and cosine curves -> amplitude = |a|
and to define a period of sine and cosine curves ->

Today we did a warm-up with a liftoff function. example: g5(125)= g5(5^3)=3. Then we had to sketch y=4^x and use it to sketch a graph of a) y= 4^(-x) - 3, b) y=16*4^x and c) y=4^(0.5x). In b) 16=4^2 which makes y=4^2 + 4^x = 4^(x+2). In c) 4=2^2 which makes y= (2^2)^(0.5x)= 2^x. Then we discussed exercises 55 and 59 from hw. We used a formula A=P(1 + (r/n))^nt and GDC. Then we also used A=Pe^(rt) formula. Then we did the last page of Mystery function. Then we realized that mystery function and liftoff function is log. Definition: x=b^y means the same as y=log (b)^x. We went to http://www.purplemath.com/modules/logs.htm.
example: log(27)^9, in words: "The power you raise 27 to to get 9"
Then we found the inverse of exponential: f(x)=b^x then: y=b^x, then inverse: x=b^y, then solve for y: y= log(b)^x. So f^(-1)(x)=log (b)^x