Question

Given csc(A) = 60/16 and that angle A is in Quadrant I, find the exact value of sec A in simplest radical form using a rational denominator . Someone please help me!

Answer 1

Answer:

$\displaystyle \sec A=\frac{65}{63}$

Step-by-step explanation:

We are given that:

$\displaystyle \csc A=\frac{65}{16}$

Where A is in QI.

And we want to find sec(A).

Recall that cosecant is the ratio of the hypotenuse to the opposite side. So, find the adjacent side using the Pythagorean Theorem:

$a=\sqrt{65^2-16^2}=\sqrt{3969}=63$

So, with respect to A, our adjacent side is 63, our opposite side is 16, and our hypotenuse is 65.

Since A is in QI, all of our trigonometric ratios will be positive.

Secant is the ratio of the hypotenuse to the adjacent. Hence:

$\displaystyle \sec A=\frac{65}{63}$

Answer 2

Answer:

Step-by-step explanation:

cosec A =60/16

hypotenuse/opposite = 60/16 =15/4 (in simplest form)

therefore hypotenuse = 15 , opposite = 4  

then adjacent =? (let be x)

using pythagoras theorem to find adjacent

opposite^2 + adjacent^2 = hypotenuse^2

4^2 + x^2 = 15^2

16 + x^2 = 225

x^2 = 225 - 16

x^2 = 209

$x=\sqrt{209}$

sec A =hypotenuse/adjacent

$=\frac{15}{\sqrt{209} }$

$=\frac{15}{\sqrt{209} } * \frac{\sqrt{209} }{\sqrt{209} }$

=$\frac{15\sqrt{209} }{209}$