Question

1. (43) use the mnemonic “oscar had a hold on arthur” as an aid in writing the definitions of sine a, cosine a, and tangent a. algebra 2 lesson 43

Explanation:

Step1: Recall mnemonic mapping

"Oscar had a hold on Arthur" breaks to:

• O = Opposite, H = Hypotenuse, A = Adjacent
• Oscar: Over Hypotenuse (sine)
• had a hold: Adjacent Over Hypotenuse (cosine)
• on Arthur: Opposite Over Adjacent (tangent)

Step2: Define sine A

Sine uses opposite over hypotenuse.
$\sin A = \frac{\text{Opposite side to } A}{\text{Hypotenuse}}$

Step3: Define cosine A

Cosine uses adjacent over hypotenuse.
$\cos A = \frac{\text{Adjacent side to } A}{\text{Hypotenuse}}$

Step4: Define tangent A

Tangent uses opposite over adjacent.
$\tan A = \frac{\text{Opposite side to } A}{\text{Adjacent side to } A}$

Answer:

$\sin A = \frac{\text{Opposite to } A}{\text{Hypotenuse}}$
$\cos A = \frac{\text{Adjacent to } A}{\text{Hypotenuse}}$
$\tan A = \frac{\text{Opposite to } A}{\text{Adjacent to } A}$