Question

Select the correct trigonometric ratios for angle 0

Answer 1

Answer:

A, D, and F

Step-by-step explanation:

First off, we're not given the hypotenuse's length, so let's use the Pythagorean Theorem to find it:

$1^2+3^2=c^2\\1+9=c^2\\10=c^2\\c=\sqrt{10}$

With that, we can refer to SOH-CAH-TOA to help us find sine, cosine, and tangent:

SOH (Sine = Opposite/Hypotenuse)

$\sin{\theta}=1/\sqrt{10}=\sqrt{10}/10$

CAH (Cosine = Adjacent/Hypotenuse)

$\cos{\theta}=3/\sqrt{10}=3\sqrt{10}/10$

TOA (Tangent = Opposite/Adjacent)

$\tan{\theta}=1/3$

From this, we can see that A matches up with sine, and we can eliminate B and C.

Cosecant, secant, and cotangent are all reciprocals of the three basic trig ratios:

$\csc{\theta}=1/\sin{\theta}=\sqrt{10}\\\sec{\theta}=1/\cos{\theta}=\sqrt{10}/3\\\cot{\theta}=1/\tan{\theta}=3$

D matches with cosecant, and F matches with cotangent, so the correct trig rations for θ are A, D, and F.