Arc Trigonometry
Practice
For practice try the following:
4.1 Given: 
a) State the domain:
where 
can never be greater than 1 or less than negative 1
b) State the range:
range of 
range of 
Where a = anything
c) Evaluate 
d) Give the equation of the tangent line at 
4.2 Given: 
a) Is 
increasing or decreasing for all x?
will always be negative and 
will always be positive so the slope will be negative.
If the slope is negative then 
will be always decreasing.
b) Give the equation of the horizontal asymptotes.
These refer to y values that will never exceed. This is very similar to asking for the range of . Range: 
So the equations of the asymptotes are: 
c) Find 
4.3 Multiple Choice: 
equals:
a. 
b. 
c. 
d. 
Where θ = the angle is a right triangle opposite leg = x, the adjacent leg = 1 and the hypotenuse =
So choice (a) is correct
4.4 Given 
Find 
4.5 
Find 
4.6 Given 
Solve for the relative minimum and relative maximum (x.y). Label them as min. or max.
To find relative min, max calculate 
, when is positive it’s a relative minimum and when its negative it is a relative maximum.
Since negative it’s a rel. max
Since positive it’s a rel. min
Relative minimum: 
Relative maximum: 
4.7 Given 
find 
4.8 Find 
4.9 Find 
4.10 Find 
4.11 Evaluate 
4.12 Evaluate 
4.13 Find 
4.14 Find 
4.15 Find the average slope for 
on 
Average slope = 
4.16 Find b if 
