3 years ago

How to find the relative maximum and minimum of a function?

Mathematics

1 answer:

antiseptic1488 [7]3 years ago

4 0

Use socratic to find your answer! :)

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Angle A is in standard position and terminates in quadrant IV. If sec(A)=4/3, complete the steps to find cot(A).

Butoxors [25]

Answer:

Part A) Use the identity $tan^2(A)+1=sec^2(A)$

Part B) $cot(A)=-\frac{3\sqrt{7}}{7}$

Step-by-step explanation:

we know that

$tan^2(A)+1=sec^2(A)$ ----> by trigonometric identity

we have

$sec(A)=\frac{4}{3}$

substitute in the expression above

$tan^2(A)+1=(\frac{4}{3})^2$

solve for tan(A)

$tan^2(A)+1=\frac{16}{9}$

$tan^2(A)=\frac{16}{9}-1$

$tan^2(A)=\frac{7}{9}$

square root both sides

$tan(A)=\pm\frac{\sqrt{7}}{3}$

Remember that Angle A terminates in quadrant IV

The value of tan(A) is negative

$tan(A)=-\frac{\sqrt{7}}{3}$

<em>Find the value of cot(A)</em>

we know that

$cot(A)=\frac{1}{tan(A)}$ ----> is the reciprocal

therefore

$cot(A)=-\frac{3}{\sqrt{7}}$

simplify

$cot(A)=-\frac{3\sqrt{7}}{7}$

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Answer:

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Parallelogram = 6*5 = 30

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