2. HOW TO MEASURE IN BOTH DEGREES AND
RADIANS
A degree is a measurement you use in angles. One
way that you can get an angle is using sine, cosine,
or tangent inverse.
A radian is when the measure is 1 radian for the
central angle of a circle if it shows an arc with the
same length like the radius.
3. KNOW THE CONVERSION BETWEEN DEGREES
AND RADIAN MEASURE
To convert radians to degrees, you have to multiply
180÷π radians
Example- 3 π rad × 180° (3/4)×180= 135°
4 π rad
To convert degrees to radians, you must multiply π
radians÷180
Example- 60° × π rad =60 π rad= π/3 rad
1 180° 180°
5. THEIR DEFINITION AS X- & Y-COORDINATES ON
THE UNIT CIRCLE
Sine=y
Cosine=x
Example: 5π/6 is equal to 150° and the point is
(-√3/2,1/2)
Sine would equal 1/2 , while cosine equals -√3/2
6. STUDENTS ARE CAPABLE OF COMPUTING UNKNOWN
SIDES OR ANGLES IN A RIGHT TRIANGLE.
In order to find a side of a right triangle you can use the Pythagorean
Theorem, which is a^2+b^2=c^2. The a and b represent the two shorter sides
and the c represents the longest side which is the hypotenuse.
Example- if you have to sides with the measurement of 3 and 5 and you
are trying to fine the hypotenuse then you would use the formula
3^2+5^2=c^2 . You will get 9+25=c^2 and then 34=c^2 and you would
have to square both sides and you get the hypotenuse (c)
To get the angle of a right angle you can use sine, cosine, and tangent
inverse. They are expressed as tan^(-1) ,cos^(-1) , and sin^(-1) .
Example- if you want to fine the angle across from three on the right
angle above then you would use tangent inverse. It would be tan A=3/5
and then you multiply both sides by tan^(-1) and you get tan^(-1) 〖
(3/5)〗. You put that in the calculator and you get side A.
7. STUDENTS USE TRIGONOMETRY IN A VARIETY
OF WORDS PROBLEMS.
Example- “Suppose you are standing on one bank of a river. A
tree on the other side of the river is known to be 150 ft. tall. A
lone from the top of the tree to the ground at your feet makes
an angle of 11° with the ground. How far from you is he base
of the tree?”
(x)tan11°=150/x (x)
.19x/.19=150/.19 150 ft
x=789.47 ft. 11° x
Word problems are expressed to show real life situations. Word
problems are usually more difficult than a problem from the
actual lesson. The word problems we do are the same as the
problems we usually do but it just requires more thinking.
8. UNIT 2
Functions of the form f(t)=A sin (Bt + C) &
f(t)=A cos (Bt + C):
4.4, 4.5, 4.7, 4.8
10. STUDENT WILL BE ABLE TO TAKE A GIVEN ANGLE AND COMPUTE THE
TRIGONOMETRIC FUNCTION AND ITS INVERSE WITH THE AID OF THE UNIT
CIRCLE (BY HAND)
11. STUDENTS USE TRIGONOMETRY IN A VARIETY
OF WORD PROBLEMS.
“When sitting atop a tree and looking down at his pal Joey, the angle
of depression of Mack’s line of sight is 38°32’. If joey is know to be
standing 39 feet from the base of the tree, how tall is the tree ?
h
39 ft 38°32’
First you must convert the 32 into degrees so you divide
it by 60 and then add it to 38 and you get 38.5°.
Then to get the height you have to use tangent and you
use tan38.5°=h/39 and you get the height of the tree to
be approximately 31 ft.
21. VECTORS-ADDITION AND SCALAR
MULTIPLICATION
U=(u1,u2), v=(v1,v2) are vectors. When you are adding you
use the formula u+v=(u1+v1,u2,v2). K is known to be a real
number and you would use it to multiply with the formula
ku=k(u1,u2)=<ku1,ku2>.
Example- let u=<-1,3> and v=<4,7> and add the vectors.
u+v=(-1,3)+(4,7)=(-1+4,3+7) <-3,10>
All you have to do is add the first number from each point
to get the x and add the second number from each point
together to get the y.
Example- use scalar multiplication to find 3u when
u=<-1,3>.
Since there is a 3 before the u, you have to multiply each
number in the point by three.
3u=3(-1,3)=(-3,9)
22. VECTORS-RESOLVING THE VECTOR
The formula v=(|v|cosƟ,|v|sinƟ) can be used when v has a
direction angle Ɵ and the components of v can be calculated.
The unit vector in the direction of v is u=v/|v|=(cosƟ,sinƟ).
Example- “find the components of vector v with direction angle
115 and magnitude 6.”
All you have to do is substitute 6 which is the magnitude
into the equation wherever there is a v. Also plug in 115
wherever there is a Ɵ.
V=(a,b)=(6cos115 ,6sin115 ) a would be approximately -
2.54 while b would be about 5.44