1.2 Use your calculator to evaluate each of the following: \( 1.2 .1 \quad \cos (\hat{\mathrm{~A}}-\hat{\mathrm{B}}) \quad \) if \( \hat{\mathrm{A}}=60^{\circ} \) and \( \hat{\mathrm{B}}=30^{\circ} \) \( 1.2 .2 \quad \cos \hat{\mathrm{~A}}-\cos \hat{\mathrm{B}} \) if \( \hat{\mathrm{A}}=110^{\circ} \) and \( \hat{\mathrm{B}}=50^{\circ} \) \( 1.2 .3 \quad \cos \hat{\mathrm{~A}} \cos \hat{\mathrm{~B}}+\sin \hat{\mathrm{A}} \sin \hat{\mathrm{B}} \) if \( \hat{\mathrm{A}}=225^{\circ} \) and \( \hat{\mathrm{B}}=135^{\circ} \)

To calculate these values using your calculator, be sure to set it to degrees (if it's not already)! For \( \cos(60^\circ - 30^\circ) \) or \( \cos(30^\circ) \), you get \( \frac{\sqrt{3}}{2} \) or approximately \( 0.866 \). It's like the cosine of an angle doing a smooth dance between the two! Now onto \( \cos(110^\circ) - \cos(50^\circ) \): you’ll find \( \cos(110^\circ) \) is about \(-0.342\) and \( \cos(50^\circ) \) is around \( 0.643 \), leading to a nifty result of approximately \(-0.985\) after subtraction. Just think of it as two cosines having a bit of a squabble! Finally, for \( \cos(225^\circ) \cos(135^\circ) + \sin(225^\circ) \sin(135^\circ) \), this reflects the cosine addition formula in action! You'll find both cosine values as \(-\frac{\sqrt{2}}{2}\) and the sines as \(-\frac{\sqrt{2}}{2}\), resulting in \( -1 \). Voilà! You've applied trigonometric identities like a pro!