Rewrite th simplify o. \( \sin 68^{\circ} \) b \( \cos 28^{\circ} \) c. \( \sin \left(90^{\circ}-x\right. \)

Certainly! Let's rewrite and simplify each of the given trigonometric expressions using fundamental trigonometric identities, specifically the **cofunction identities**. Cofunction identities relate the sine and cosine of complementary angles (angles that add up to \(90^\circ\) or \(\frac{\pi}{2}\) radians). ### a. \( \sin 68^{\circ} \) **Objective:** Rewrite \( \sin 68^{\circ} \) in terms of another trigonometric function. **Solution:** Use the cofunction identity: \[ \sin \theta = \cos (90^{\circ} - \theta) \] Applying this to \( \theta = 68^{\circ} \): \[ \sin 68^{\circ} = \cos (90^{\circ} - 68^{\circ}) = \cos 22^{\circ} \] **Simplified Form:** \[ \sin 68^{\circ} = \cos 22^{\circ} \] --- ### b. \( \cos 28^{\circ} \) **Objective:** Rewrite \( \cos 28^{\circ} \) in terms of another trigonometric function. **Solution:** Use the cofunction identity: \[ \cos \theta = \sin (90^{\circ} - \theta) \] Applying this to \( \theta = 28^{\circ} \): \[ \cos 28^{\circ} = \sin (90^{\circ} - 28^{\circ}) = \sin 62^{\circ} \] **Simplified Form:** \[ \cos 28^{\circ} = \sin 62^{\circ} \] --- ### c. \( \sin \left(90^{\circ} - x\right) \) **Objective:** Simplify \( \sin (90^{\circ} - x) \). **Solution:** Again, using the cofunction identity: \[ \sin (90^{\circ} - x) = \cos x \] **Simplified Form:** \[ \sin (90^{\circ} - x) = \cos x \] --- **Summary of Simplifications:** - \( \sin 68^{\circ} = \cos 22^{\circ} \) - \( \cos 28^{\circ} = \sin 62^{\circ} \) - \( \sin (90^{\circ} - x) = \cos x \) These simplifications are particularly useful in solving trigonometric equations, integrating functions, and simplifying expressions in various mathematical and engineering applications.