How do i solve this?
1 answer:
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Answer:
Step-by-step explanation:
Given
Required
Solve (a) to (d)
Using tan formula, we have:
This gives:
Rewrite as:
Using a unit ratio;
Using Pythagoras theorem, we have:
Take square roots of both sides
So, we have:
Solving (a):
This is calculated as:
Where:
So:
Solving (b):
This is calculated as:
Where:
---- given
So:
Solving (c):
In trigonometry:
Hence:
Solving (d):
This is calculated as:
Where:
So:
The general form of a quadratic (second degree) equation is
, where
is called the Discriminant.
The Discriminant determines how many roots the equation will have as follows:
i) if D>0, the equation has 2 roots.
ii) if D=0, the equation has 1 double root.
iii) if D<0, the equation has no roots.
In our equation,
, a=1, b=-5, c=7
so the discriminant is D=(-5)^2-4*1*7=25-28<0
Thus the equation has no roots.
Remark: the equation has no roots in the Real numbers, but it has 2 roots in a larger set of numbers to be discussed in the future, the Complex numbers.
The Discriminant determines how many roots the equation will have as follows:
i) if D>0, the equation has 2 roots.
ii) if D=0, the equation has 1 double root.
iii) if D<0, the equation has no roots.
In our equation,
so the discriminant is D=(-5)^2-4*1*7=25-28<0
Thus the equation has no roots.
Remark: the equation has no roots in the Real numbers, but it has 2 roots in a larger set of numbers to be discussed in the future, the Complex numbers.