If \( \tan (t) \approx 1.6 \), and \( \sin (t) \approx 0.85 \), find \( \cos (t) \). Round to 2 decimal places. \( \cos (t) \approx \)

To find \( \cos(t) \), we can use the Pythagorean identity \( \sin^2(t) + \cos^2(t) = 1 \). Given that \( \sin(t) \approx 0.85 \), we first calculate \( \sin^2(t) \): \[ \sin^2(t) \approx 0.85^2 = 0.7225 \] Now, we can find \( \cos^2(t) \): \[ \cos^2(t) = 1 - \sin^2(t) \approx 1 - 0.7225 = 0.2775 \] Next, we take the square root to find \( \cos(t) \): \[ \cos(t) \approx \sqrt{0.2775} \approx 0.5267 \] Rounding to two decimal places: \[ \cos(t) \approx 0.53 \]