If \( \sin 40^{\circ}=p \), write EACH of the following in terms of \( p \). \( 5.1 .1 \quad \sin 220^{\circ} \) \( 5.1 .2<\cos ^{2} 50^{\circ} \) 5040

Rewrite the angle by following steps: - step0: Convert to radians: \(50^{\circ}\) - step1: Convert to radians: \(\frac{5\pi }{18}\) Rewrite the number \( 220^{\circ} \). Rewrite the angle by following steps: - step0: Convert to radians: \(220^{\circ}\) - step1: Convert to radians: \(\frac{11\pi }{9}\) To express \( \sin 220^{\circ} \) and \( \cos^{2} 50^{\circ} \) in terms of \( p \) where \( p = \sin 40^{\circ} \), we will follow these steps: ### Step 1: Calculate \( \sin 220^{\circ} \) Using the sine function's periodic properties, we can express \( \sin 220^{\circ} \) as follows: \[ \sin 220^{\circ} = \sin(180^{\circ} + 40^{\circ}) = -\sin 40^{\circ} \] Thus, we have: \[ \sin 220^{\circ} = -p \] ### Step 2: Calculate \( \cos^{2} 50^{\circ} \) Using the co-function identity, we know that: \[ \cos 50^{\circ} = \sin(90^{\circ} - 50^{\circ}) = \sin 40^{\circ} \] Therefore, we can express \( \cos^{2} 50^{\circ} \) as: \[ \cos^{2} 50^{\circ} = \sin^{2} 40^{\circ} = p^{2} \] ### Final Results 1. \( \sin 220^{\circ} = -p \) 2. \( \cos^{2} 50^{\circ} = p^{2} \) These are the expressions in terms of \( p \).