Sine Functions
What is the domain of f(x)=sin(x)?
The domain is (-∞, ∞)
What is the domain of f(x)=cos(x)?
domain (-∞, ∞)
Define a periodic function.
A periodic function is a function that repeats its values at regular intervals.
What is the domain of f(x)=tan(x)?
the domain is all real numbers except π/2=
(-∞, π/2)U(π/2, ∞)
Simplify to one identity;
tan(x)cos(x)
sin(x) because,
tan(x)cos(x)=(sin(x)/cos(x))(cos(x))=sin(x)
What is the range of f(x)= sin(x)?
The Range is (-1, 1)
What is the range of f(x)=cos(x)?
Range (-1, 1)
Give an example of a periodic function.
f(x)=sin(x) ,f(x)= cos(x) or f(x)=tan(x)
What is the range of f(x)=tan(x)?
Range (-∞, ∞)
Simplify to one identity;
cos(x)csc(x)
cot(x)
What is the reciprocal of f(x)=sin(x)?
f(x)= csc(x)= 1/sin(x)
What is the reciprocal of f(x)=cos(x)?
f(x)=sec(x)=1/cos(x)
What is the equation to find an amplitude on a periodic function?
amplitude=(max-min)/2
What is the reciprocal of f(x)=tan(x)
f(x)=cot(x)=1/tan(x)
If tan(x)=1, what is x?
x=π/4
What is sin(7π/6)?
sin (7π/6)=-1/2
What is cos(11π/6)?
cos(11π/6)=√3/2
A Ferris wheel has a diameter of 40 ft and stands 5 ft above the ground. As it rotates, the height of a particular seat above the ground is changing. It takes 1 minute for the Ferris wheel to make 1 complete revolution. How high is a rider at 30 seconds?
45 ft
What is tan(0)?
tan(0)=sin(0)/cos(0)=0/1=0
Simplify to one idea:
sin(x)sec(x)
tan(x)
csc(π/2)=1
What is sec(2π/3)?
sec(2π/3)=-2
The London Eye is a huge Ferris wheel with diameter 135 meters (443 feet) in London, England, which completes one rotation every 30 minutes. If the distance from the ground is 10 ft, how high is a rider in 7 minutes and 30 seconds?
231.5 ft high
What is cot(0)?
cot(0)=cos(0)/sin(0)=1/0=undefined
What is cos²(x)+sin²(x)?
1