Sinusoidal functions
Quadratic functions
Trigonometry
Key words: Definitions
100

What is a sinusoidal function:

A sinusoidal function is a function using the sine function
100

What is a function?

A relationship or expression involving one or more variables.

100

Which is the longest side on a triangle

Hypotenuse

100

Domain and range:

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.



200

What is the sinusoidal function format?

y = A sin (B(x - C)) + D is a general format for a sinusoidal function.

200

Example of a function:

X  Y

x1-A

x2-B

x3-C

(each X has its own Y)

200

What does SOH CAH TOA stand for

Sin opposite over hypotenuse, cos adjacent over hypotenuse, tan opposite over adjacent 

200

Sin, cos, tan

sin = o / h. The ratio of the adjacent side of a right triangle to the hypotenuse is called the cosine and given the symbol cos. cos = a / h. Finally, the ratio of the opposite side to the adjacent side is called the tangent and given the symbol tan.
300

Determine the range of each sinusoidal function without graphing. 

a) y 5 23 sin(4x) 1 2 


b)y 5 0.5 cos(3(x 2 40°))

a) 5 yER | 21<y< 56
 b) 5 yER | 20.5 <y<0.56
300

Factor:

6x² + 11x - 35 = 0

(3x−5)(2x+7)

300

Find angle "A" if you have the opposite of 4 and adjacent 8.

26.5= 27° 

300

Peak, Trough

The highest and lowest points.

peak= highest

trough=lowest

400

Determine the coordinates of the point after a rotation of about (0, 0) from the point (7, 0).

(2.96, 6.34)

400

Solve:

2x² - 4x - 2 = 0

2.4

-0.4

400

A 3m ladder can be used safely only at an angle of 75° with the horizontal. How high, to the nearest meter, can the ladder reach?

3m

400

Periodic function

This is a function that repeats.

500

Summarize how you can determine the equation of a sinusoidal function that represents real phenomena from data, a graph, or a description of the situation. In your summary, explain how each part of the equation relates to the characteristics of the graph.

To determine the equation of a sinusoidal function, first calculate the period, amplitude, and equation of the axis. This information will help you determine the values of k, a, and c, respectively, in the equations g(x) 5 a sin(k(x 2 d )) 1 c and h(x) 5 a cos(k(x 2 d )) 1 c.

500

Why might someone chose to write a curve of good fit in vertex form rather than factored form?

It is easier to used vertex form to find the max/min and the vertex

500

A weather balloon at a height of 117m has an angle of elevation of 41° from on station and 62°  from another station. If the balloon is directly above the line joining the stations, how far apart, to the nearest meter, are the two stations.

197m

500

What is a transformation and give at least 3 examples

A transformation is a change or movement in a function.

3 examples: A shift to the left, a vertical shift up 1 unit and a reflection.

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