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
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