UNIT 1
ANGLES AND RADIANS
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
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
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
*** 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
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
UNIT 2 POWERPOINT
https://docs.google.com/presentation/d/1qV8_lz8M-Tb_Bf6VUICg8DMrpA7q_nIXGzQUUJGK9jY/edit#slide=id.p | |
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