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
.
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits