UNIT 1
ANGLES AND RADIANS
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An angle is a space formed from two lines or rays that come from the same point that is measured in degrees. A radian a form of measurement whose arc is equal to the radius of the circle. In an entire circle the largest radian is 2π and it is equal to 1 or 360 degrees.
HOW TO CONVERT DEGREES TO RADIANS and radians to degrees
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The general formula for finding the radians in a certain degree is: degrees * (π/180)= radians. The general formula for finding the degrees in a certain radian is: radians*(π/180)= degrees
AXIS OF COSINE AND SINE ON THE UNIT CIRCLE
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On the unit circle cosine is defined as the horizontal coordinate of an angle. This would mean that sine is defined as the vertical coordinate of the same angle. The y-axis is equal to sine because its side is opposite to the central angle while the side of cosine along the x-axis is adjacent to the central angle
GRAPHS AND CHARACTERISTICS OF COSINE AND SINE FUNCTIONS
COSINE GRAPH
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SINE GRAPH
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FINDING ANGLES AND SIDES OF A RIGHT TRIANGLE WITH COSINE AND SINE
![Picture](/uploads/1/9/4/7/19470175/373606762.gif)
*** to find the missing side of a triangle use the formula: a^2 + b^2 = c^2
a & b represent the adjacent and opposite sides while c represents the hypotenuse
ex) finding the hypotenuse using cosine
using cosine
1) 400^2 + 300^2= c^2
2) 160,000 + 90,000 = c^2
3) 250,000=c^2
500=c
*** to find the angle of a triangle you must use the inverse function of cosine and sine
* the inverse function of cosine is sec= hypotenuse/ adjacent
* the inverse function of sine is csc= hypotenuse/ opposite
a & b represent the adjacent and opposite sides while c represents the hypotenuse
ex) finding the hypotenuse using cosine
using cosine
1) 400^2 + 300^2= c^2
2) 160,000 + 90,000 = c^2
3) 250,000=c^2
500=c
*** to find the angle of a triangle you must use the inverse function of cosine and sine
* the inverse function of cosine is sec= hypotenuse/ adjacent
* the inverse function of sine is csc= hypotenuse/ opposite
finding csc and sec
![Picture](/uploads/1/9/4/7/19470175/272375176.jpg?278)
ex) find the value of the angle given that there is a triangle with an angle of 60 degrees, 30 degrees, a hypotenuse of 2, and an adjacent side of 1
using cosine and sine in the real world
in order to find the height of the tree lets first use cosine 31.8 = 71/h to find the height of the hypotenuse. first move the value of h to the side where cosine is at. You would now have h cosine 31.8 = 71. Now divide 71 by cosine 31. 8 degrees. You should get 83.53 ft. Next use sine 31.8= y / 83.53 to get the height of the tree. First you should get 83.53 sine 31.8 = y. When you calculate it, the tree should have a height of y= 31.29 ft
UNIT 4
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UNIT 2 POWERPOINT
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