How can the graph of
be used to construct the graph of
Explain why the period of
is equal to
Answers will vary. Using the unit circle, one can show that
Why are there no intercepts on the graph of
How does the period of
compare with the period of
The period is the same:
Algebraic
For the following exercises, match each trigonometric function with one of the following graphs.
IV
III
For the following exercises, find the period and horizontal shift of each of the functions.
period: 8; horizontal shift: 1 unit to left
If
find
1.5
If
find
If
find
5
If
find
For the following exercises, rewrite each expression such that the argument
is positive.
Graphical
For the following exercises, sketch two periods of the graph for each of the following functions. Identify the stretching factor, period, and asymptotes.
stretching factor: 2; period:
asymptotes:
stretching factor: 6; period: 6; asymptotes:
stretching factor: 1; period:
asymptotes:
Stretching factor: 1; period:
asymptotes:
stretching factor: 2; period:
asymptotes:
stretching factor: 4; period:
asymptotes:
stretching factor: 7; period:
asymptotes:
stretching factor: 2; period:
asymptotes:
stretching factor:
period:
asymptotes:
For the following exercises, find and graph two periods of the periodic function with the given stretching factor,
period, and phase shift.
A tangent curve,
period of
and phase shift
A tangent curve,
period of
and phase shift
For the following exercises, find an equation for the graph of each function.
Technology
For the following exercises, use a graphing calculator to graph two periods of the given function. Note: most graphing calculators do not have a cosecant button; therefore, you will need to input
as
Graph
What is the function shown in the graph?
Real-world applications
The function
marks the distance in the movement of a light beam from a police car across a wall for time
in seconds, and distance
in feet.
Graph on the interval
Find and interpret the stretching factor, period, and asymptote.
Evaluate
and
and discuss the function’s values at those inputs.
Standing on the shore of a lake, a fisherman sights a boat far in the distance to his left. Let
measured in radians, be the angle formed by the line of sight to the ship and a line due north from his position. Assume due north is 0 and
is measured negative to the left and positive to the right. (See
[link] .) The boat travels from due west to due east and, ignoring the curvature of the Earth, the distance
in kilometers, from the fisherman to the boat is given by the function
What is a reasonable domain for
Graph
on this domain.
Find and discuss the meaning of any vertical asymptotes on the graph of
Calculate and interpret
Round to the second decimal place.
Calculate and interpret
Round to the second decimal place.
What is the minimum distance between the fisherman and the boat? When does this occur?
and
the distance grows without bound as
approaches
—i.e., at right angles to the line representing due north, the boat would be so far away, the fisherman could not see it;
3; when
the boat is 3 km away;
1.73; when
the boat is about 1.73 km away;
1.5 km; when
A laser rangefinder is locked on a comet approaching Earth. The distance
in kilometers, of the comet after
days, for
in the interval 0 to 30 days, is given by
Graph
on the interval
Evaluate
and interpret the information.
What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond?
Find and discuss the meaning of any vertical asymptotes.
A video camera is focused on a rocket on a launching pad 2 miles from the camera. The angle of elevation from the ground to the rocket after
seconds is
Write a function expressing the altitude
in miles, of the rocket above the ground after
seconds. Ignore the curvature of the Earth.
Graph
on the interval
Evaluate and interpret the values
and
What happens to the values of
as
approaches 60 seconds? Interpret the meaning of this in terms of the problem.
after 0 seconds, the rocket is 0 mi above the ground;
after 30 seconds, the rockets is 2 mi high;
As
approaches 60 seconds, the values of
grow increasingly large. The distance to the rocket is growing so large that the camera can no longer track it.
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities.
before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
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