Angle A is in standard position and terminates in quadrant IV. If sec(A)=4 3 , complete the steps to find cot(A). Use the identi
2 answers:
If sec(A) = 4/3, then the value cot(A) is
The given trigonometric identity is:
.........................(*)
Note that:
.........................(**)
Comparing (*) and (**)
Hypotenuse = 4
Adjacent = 3
Find the opposite using the Pythagoras theorem
Hypotenuse² = Opposite² + Adjacent²
4² = Opposite² + 3²
Opposite² = 4² - 3²
Opposite² = 16 - 9
Opposite² = 7
Opposite = √7
cot(A) = Adjacent/Opposite
cot(A) = 3/√7
Rationalize the expression
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The domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.
<h3>What is a function?</h3>It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
f(x) = 1/√x
m(x) = x² - 4
Domain of f(x)/m(x):
f(x)/m(x) = (1/√x)/(x² - 4)
f(x)/m(x) = 1/√x(x² - 4)
The denominator cannot be zero:
√x(x² - 4) ≠ 0
x(x - 2)(x+2) ≠ 0
x ≠ 0, 2, -2
and x > 0
Domain of f(x)/m(x) is: (0, ∞) - {0, 2, -2} or
Domain of f(m(x)):
f(m(x)) = 1/√(x² - 4)
x² - 4 > 0
Domain:
Domain of m(f(x)):
= ((1/√x)² - 4)
Domain:
Thus, the domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.
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Answer: The inverse of the given function is
Step-by-step explanation: We are given to find the inverse of the following linear function :
The inverse of y = f(x) is written as
Substituting the above in equation (i), we get
Thus, the inverse of the given function is