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Tornenork Faluate, what using a calculator (a) \( \tan 315^{\circ}-2 \cos 60^{\circ}+\sin 210 \) (b) \( \frac{\tan 150^{\circ}}{\tan 240^{\circ}}-\frac{\sin 300^{\circ}}{\sin 120^{\circ}} \) (c) \( \frac{\tan 225^{\circ}-\sin x}{\sin x+\sin 270^{\circ}} \) (b) \( \sin 570^{\circ}+\cos 240^{\circ}-\tan 135^{\circ} \) (c) \( \tan 120^{\circ} \cdot \cos 210^{\circ}-\sin ^{2} 315^{\circ} \)

Ask by Tucker Dunn. in South Africa
Mar 15,2025

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Answer

**(a)** \( -\frac{5}{2} \) **(b)** \( \frac{2}{3} \) **(c)** \( -1 \) (when \( \sin x \neq 1 \)) **(d)** \( 0 \) **(e)** \( 1 \)

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To make your calculations easier, remember that using a scientific calculator can help you quickly evaluate trigonometric functions, especially for angles beyond the first quadrant. For example, key in \( \tan(315) \), currently find \( -2 \cos(60) \), and add \( \sin(210) \); your calculator will spit out results in no time, ensuring you're not adding or subtracting angles in your head! Also, common pitfalls include forgetting to adjust angles that exceed 360°. For instance, \( \sin(570^{\circ}) \) can be simplified to \( \sin(210^{\circ}) \) since \( 570 - 360 = 210 \). This can prevent mix-ups, especially when working with multiple operations. Keep track of your angle measures, and you’ll avoid those sneaky mistakes!

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