Investigation : reduction formulae for function values of
Function values of
In the figure P and P' lie on the circle with radius 2. OP makes an angle
with the
-axis. P thus has coordinates
. P' is the reflection of P about the
-axis or the line
. Using symmetry, write down the coordinates of P'.
Using the coordinates for P' determine
,
and
.
From your results try and determine a relationship between the function values of
and
.
It is possible to have an angle which is larger than
. The angle completes one revolution to give
and then continues to give the required angle. We get the following results:
Note also, that if
is any integer, then
Write
as the function of an acute angle.
where we used the fact that
. Check, using your calculator, that these values are in fact equal:
Evaluate without using a calculator:
Reduction formulae
Write these equations as a function of
only:
Write the following trig functions as a function of an acute angle:
Determine the following without the use of a calculator:
Determine the following by reducing to an acute angle and using special angles. Do not use a calculator:
Function values of
When the argument of a trigonometric function is
we can add
without changing the result. Thus for sine and cosine
Function values of
Investigation : reduction formulae for function values of
Function values of
In the figure P and P' lie on the circle with radius 2. OP makes an angle
with the
-axis. P thus has coordinates
. P' is the reflection of P about the line
. Using symmetry, write down the coordinates of P'.
Using the coordinates for P' determine
,
and
.
From your results try and determine a relationship between the function values of
and
.
Function values of
In the figure P and P' lie on the circle with radius 2. OP makes an angle
with the
-axis. P thus has coordinates
. P' is the rotation of P through
. Using symmetry, write down the coordinates of P'. (Hint: consider P' as the reflection of P about the line
followed by a reflection about the
-axis)
Using the coordinates for P' determine
,
and
.
From your results try and determine a relationship between the function values of
and
.
Questions & Answers
I'm interested in biological psychology and cognitive psychology
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.
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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