PreCalculus Chpt 4
Table of Contents
- Section 4.5
- Graph y = a sin(x) + d (Quiz)
- Sliders and Trig Functions
- Sine & Cosine Function Modeling: Finding Correct Parameters
- Bugs on Circle
- Section 4.6
- Trig graphs
- Sec 6.1 Law of Sines
- Law of Sines (& Area)
- Sec 6.2 Law of Cosines
- Law of Cosines: Discovery
Graph y = a sin(x) + d (Quiz)
[color=#c51414][b]Directions:[/b][/color][br][br]1) [color=#0a971e]Note the sine function displayed in green in the upper right hand corner of the applet.[/color][br]2) Move each of the [color=#c51414]5 red points[/color] up and/or down so that the [color=#c51414]red wave that passes through these 5 points is the EXACT GRAPH[/color] of the [color=#0a971e]green equation[/color] displayed.[br] (There may be times when the red graph will disappear--and that's okay. It'll reappear as you continue to move these points.) [br]3) Once you graph the displayed function correctly, the entire graph will turn green and a "NICE JOB !!!" box will appear.[br]4) Click on the "Generate New Function to Graph" to display a new equation.[br]5) Repeat steps (1) - (3). Then repeat step (4). [br]6) [b]Complete this activity as many times as you need in order to master this concept! [/b][br][br][b]**For extra practice with graphing functions of the form "y = a cos(x) + d", go to http://tube.geogebra.org/m/1754109. [/b]
Trig graphs
adam caudell
Law of Sines (& Area)
Interact with the applet below for a minute. [br]Then, answer the questions that follow. [br](Please don't slide the 2nd slider until prompted to in the directions below.)
1) Take a look at the yellow right triangle on the left.[br]Write an equation that expresses the relationship among angle [i]B[/i], the triangle's height, and side [i]c[/i].
2) Rewrite this equation so that [i]height [/i]is written in terms of side [i]c[/i] and angle [i]B[/i].
3) Now consider the pink right triangle on the right. Write an equation that expresses the relationship among angle [i]C[/i], side [i]b[/i], and the triangle's height. [br]
4) Rewrite this equation so that [i]height[/i] is written in terms of side [i]b[/i] and angle [i]C[/i].
5) Take your responses to questions (2) and (4) to write a new equation that expresses the relationship among [i]C[/i], [i]B[/i], [i]c[/i], and [i]b[/i]. Write this equation so that [i]C[/i] and [i]c[/i] appear on one side of the equation and that [i]B[/i] and [i]b[/i] appear on the other.
6) Now drag the slider in the upper right hand corner. Now, given the fact that the length of segment [i]BC[/i] would be denoted as [i]a [/i](it's just not drawn in the applet above), write an expression for the area of this original triangle in terms of [i]a[/i], [i]b[/i], and [i]C[/i].
7) Same question as in (6) above, but this time write the area of the triangle in terms of [i]a[/i], [i]c[/i], and [i]B[/i].
8) Suppose that dragging the first slider dropped a height from point [i]C[/i] instead of point [i]A[/i]. Answer questions (1) - (5) again, this time letting [i]c[/i] serve as the base of this triangle (vs. side [i]a[/i]). Notice anything interesting in your results?
Law of Cosines: Discovery
[color=#000000]Interact with the applet below for a few minutes. [br]Then, answer the questions that follow. [br][/color][br]
[color=#000000](Be sure the black slider has been slid all the way to the right before answering these questions.)[/color]
1)
[color=#000000]Write an equation that expresses the relationship among [i]A, x, [/i]and [i]b[/i]. [br]Then, if necessary, rewrite this equation so that [i]x[/i] is written in terms of [i]b[/i] and [i]A[/i]. [/color]
2)
[color=#000000]Write an equation that expresses the relationship among [i]b[/i], [i]x[/i], and [i]h[/i]. [/color]
3)
[color=#000000]Without introducing a new variable, write an equation that expresses the relationship among the sides of Triangle [i]BDC[/i]. [/color]
4)
[color=#000000]Rewrite the equation you wrote in response to question (3) so that each side of the equation is written in simplest form. [/color]
5)
[color=#000000]Now use any one (or more) equations you've written in response to the questions above [/color][color=#0000ff][b]so that the equation you wrote for (4) contains no power of [i]x[/i] and no power of [i]h[/i]. [/b][/color]