Question

Check all that apply. If csc = 13/12, then:

Answer 1

Answer:

Step-by-step explanation:

I don't know where you are in your class, or even what chapter you are in, but I solved this using a right triangle.

We don't need to know the angles, just the sides.

c is the hypotenuse, the line at a tilt

b is the adjacent line, directly below c

a is the opposite line

c = 13

a= 12

b = ?

In order to find b, we use the Pythagorean Theorem, $a^{2} + b^{2} = c^{2}$, but we need to rearrange the problem to where we are solving for b instead of c, $b^{2} = a^{2} + c^{2}$

$b^{2} = (12)^{2} + (13)^{2}\\b^{2} = 144 + 169\\b^{2} = 313 \\\sqrt{b^{2} } = \sqrt{313}\\ b = 17.69$

So, b = 17.69

Now, we need to evaluate each of the trig. functions:

$sin = \frac{opposite}{hypotenuse} = \frac{12}{13} \\csc = \frac{hypotenuse}{opposite} = \frac{13}{12} \\cos = \frac{adjacent}{hypotenuse} = \frac{17.69}{13} \\sec = \frac{hypotenuse}{adjacent} = \frac{13}{17.69}\\tan = \frac{opposite}{adjacent} = \frac{12}{17.69}\\cot = \frac{adjacent}{opposite} = \frac{17.69}{12}$

So, there is your answers, hope that is what you are looking for.