V 153
Given tan A= - and that angle A is in Quadrant IV, find the exact value of
sec A in simplest radical form using a rational denominator.
4
Answers
The secant of the angle A is 13/4
How to determine the value of sec(A)?The given parameter is:
[tex]\tan(A) = -\frac{\sqrt{153}}{4}[/tex]
Using the trigonometry identity, we have:
[tex]\sec^2(A) = \tan^2(A) + 1[/tex]
This gives
[tex]\sec^2(A) = (-\frac{\sqrt{153}}{4})^2 + 1[/tex]
Evaluate the exponent
[tex]\sec^2(A) = \frac{153}{16} + 1[/tex]
Evaluate the sum
[tex]\sec^2(A) = \frac{169}{16}[/tex]
Take the square root of both sides
[tex]\sec(A) = \pm \frac{13}{4}[/tex]
Secant in quadrant IV is positive.
So, we have:
[tex]\sec(A) = \frac{13}{4}[/tex]
Hence, the secant of angle A is 13/4
Read more about trigonometry ratios at:
https://brainly.com/question/11967894
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What is arithmetic progression?
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According to the given problem,
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Number of seats in row 2 = 39
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Learn more about arithmetic progression here: https://brainly.com/question/13989292
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