ADDITION OF SINE AND COSINE: Consider the following:
g(x) =sin(x).
f(x) + cos(x)
and h(x) =f(x) +g(x)
The graph above shows the three functions.

It can be shown that the new function h(x) can be written at:
h(x) = V2sin (x +45)

1. Explain in words and show the steps on how the single trigonometric function for
h(x) could be found, using the original functions. for (9) marks

2.Write a full explanation or presentation on how the expression of
a sin(x) + b cos(x) can be written as a single trigonometric ratio. for (18) marks

3. Give the simplified expression for y = asin(x) + b cos (x) and comment on the new function's amplitude, period and shifts (vertical and horizontal) for (6) marks.

4.a. Application: Use your method above to describe how it can be used to find
the general solution for a sin(x) + b cos(x) = 0. for (4) marks

b. Give an example. for (4) marks
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Chose the graph below that represents the following system of inequality’s

Which value is not a solution of 8x^3 – 1 = 0

In tossing one coin 10 times, what are your chances for tossing a head? a tail? 2. in tossing one coin 100 times, what are your chances for tossing a head? a tail? 3. in tossing one coin 200 times, what are your chances for tossing a head? a tail? deviation = ((absolute value of the difference between expected heads and observed heads) + (absolute value of the difference between expected tails and observed tails)) divided by total number of tosses. this value should always be positive. 4. what is the deviation for 10 tosses? 5. what is the deviation for the 100 tosses? 6. what is the deviation for 200 tosses? 7. how does increasing the total number of coin tosses from 10 to 100 affect the deviation? 8. how does increasing the total number of tosses from 100 to 200 affect the deviation? 9. what two important probability principles were established in this exercise? 10. the percent of occurrence is the obtained results divided by the total tosses and multiplied by 100%. toss the coins 100 times and record your results. calculate the percent occurrence for each combination. percent head-head occurrence: percent tail-tail occurrence: percent head-tail occurrence: