# Tutoring Algebra 2 Regents

# Review

# Trigonometry Functions

__START: __To start this problem we must know what

The angle 13pi/20 represents, what is 13pi/20?

What is pi? Pi=3.18 if you said this you have no idea what the question is asking, and you should continue reading.

Pi in this case means 180 degrees; the angle in the question is in radians and contains the symbol pi.

__RULE: __

- If the angle (theta) contains the symbol pi it is represented in
.__radians__ - If the angle (theta) contains numbers only it is represented in
*degrees.*

How many degrees is 13pi/20? Do know we must convert this angle (represented in radians) to an angle represented in degrees. Only then we can locate this angle on the coordinate plane.

To convert an angle represented in radians:

Substitute pi=180 for the symbol pi.

In which quadrant is 117 degrees located?

Quadrant II. All of the choices have the image of the terminal side of the angle located in QII. So which of the choices is correct?

To eliminate choices you need to know the definition of the terminal angle.

__RULE__:

Reference angle- positive angle created from the x-axis__.__

__It is always less then 90 degrees.__

Eliminate choices 1) and 2) they do not show the reference angle created from the x-axis.

Eliminate choice 3) it shows the angle in question as negative.

Choice (4).

Amplitude – height of the given trigonometric sine graph. What is the height from the middle of the graph, break the graph horizontally in half. For the first two choices

To break a trigonometric graph count the number of graph intervals from the bottom of the graph to the top.Technique:

Choice 1) 4 total /2 ->2 amplitude

Choice 2) 8 total /2 ->4 amplitude

Choice 3) Amplitude is 3

| number in front of the trig function| – absolute number of the value in front of the trig function.

In this case the number in front of the function sine is 3, it is positive.

Amplitude – always positive.

Choice 4) Amplitude is 5

Negative number has to do with reflection of the graph across the x axis( all the y values are negated) and has no effect on the value of the amplitude.

Choice (4).

__START: __

The question is asking for the number of hours y.

The equation models the number of hours in days x. Let’s count how many days x will pass till Feb 14 2013 from January 1, 2013? 44 days .

Substitute 44 for the number of days –x.

Choice (4)

__START:__ Where is the terminal side of the angle located? In other words, where is the angle located? The x value is negative * and *the y value is negative. Which means that it has to be in QUADRANT III. Let us sketch some angles.

__Reminder: __

- Unit Circle is a circle centered in the origin with radius =1.
- Every point on the unit circle has the

(x value = cosine of the angle, y value = sine of the angle).

The angle is * not the reference angle but actual * angle in question.

-1/3 is the actual value of cos (angle in question)

-sqrt (8)/3 is the actual value of sin (angle in question).

sec(109.47)=-3.

Choice (1).

__SHORT CUT:__

If you noticed that

You would see the answer right away.

If cos (theta) = -1/3

Sec (theta) would be 1 over that, or a flipped fraction.

1/ (-1/3) = 3

Choice (1)

The question is asking for the smallest minimum value, for all the y values. In the second example this can be easily seen with the smallest q(x) value -8.

What is the smallest y value for the first function

2sin(3x)+1. This is a sine function with the amplitude 2 translated up 1 unit and period 2pi/3.

So the graph 2sin(3x) is a sine graph with the height of 2, from y value of -2 to +2.

graph 2sin(3x)+1 is a sine graph translated one unit up so the range of the y values will be from -1 to +3, and the minimum y value for the graph is -1.

Check this by graphing this function on a graphing calculator.

**Before graphing a trig function on a graphing calculator à Change mode to radian: MODEà Radian**

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