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
.
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life