CHAPTER 4 REVIEW
By: Madison, Katie, JJ, Connor, Miles, Robert
4.1- Right Triangle Trig.
Six Trig. Functions
4.2 - Degrees and Radians
Initial Side - Starting position of a ray Terminal Side - Ray’s position after
angle
rotation about the vertex
Degree - Unit of measure equivalent to 1/360 of a full rotation, helpful for
solving
real-world problems.
Radian - The angle made by taking the radius and wrapping it along the
edge of the circle.
degrees = 180°/π*radians OR radians = π/180°*degrees
Ex: Convert 100° to radians
Ex: Convert 10π/3 radians to degrees
4.2 Finding Arc Length and Area of a Sector
Arc - A segment of the circumference of the circle
Sector - A portion of the area of a circle
4.2 Examples
Ex. 1: Find the area of a
sector with an arc
length of 20 and a radius
of 10.
Ex. 2: Find arc length
4.3 - Unit Circle
Quadrantal angle: When the terminal
side of an angle theta that is in
standard position lies on one of the
coordinate axes.
Examples
Find the exact value of:
sin ( /4)
cos ( /6)
4.4 - Sine and Cosine Functions
Sine Function
Domain:
Range: [-1,1]
y-intercept: 0
x-intercepts: n
f(x)=a sin b (x-c) + d
Cosine Function
Domain:
Range: [-1,1]
y-intercept: 1
x-intercepts:
f(x)=a cos b (x-c) + d
,n
4.4 - Amplitude, Midline and Period
For sine and cosine, period = 2
/b
4.4 Examples
Sine
f(x)= sin (x+5
/6) + 4
Cosine
f(x)= cos (x/3 +
/2)
4.5 - Other Trig Functions
TANGENT GRAPH: y = a tan(b(x-c))+d
a → amplitude
b → (2π or π)/b= period
c → horizontal shift
d → vertical shift
4.5 cont.
COSECANT GRAPH:
(Reciprocal of Sine)
COTANGENT
(Reciprocal of tangent)
SECANT GRAPH:
(Reciprocal of Cosine)
4.6 - Inverse Trig Functions
-Figuring out what angle on the unit circle creates the (sin,cos, or tan) ______
4.7 - Law of Sines and Cosines
Law of Sines:
Law of Cosines :
4.7 cont.
Heron’s Formula:
Area of triangle: A= ½(b)(c)sin(A)=½(a)(b)sin(C)=½(a)(c)sin(B)
Area of right triangle: A= ½(base)(height)
4.7 Cont.
Ambiguous case – given measures of 2 sides and non included angle, either no
triangle exists, exactly 1 triangle exists, or two triangles exist.