ERCISE 2 Calculate with the use of a calculator the following rounded off to two decimal places where appropriate. \( \begin{array}{llll}\text { (1) } \cos 23^{\circ} & \text { (2) } \sin 68^{\circ} & \text { (3) } \tan 64^{\circ} \\ \text { (4) } \cos 34^{\circ} & \text { (5) } 2 \cos 45^{\circ} & \text { (6) } 5 \sin 65^{\circ} \\ \text { (7) } 7 \tan 58^{\circ} & \text { (8) }-4 \sin 30^{\circ} & \text { (9) } \frac{1}{3} \sin 70^{\circ} \\ \text { (10) } \frac{\sin 60^{\circ}}{20} & \text { (11) } \frac{\cos 24^{\circ}}{24} & \text { (12) } \tan \left(54^{\circ}+25^{\circ}\right) \\ \text { (13) } \tan 54^{\circ}+\tan 25^{\circ} & \text { (14) } \frac{40}{-25 \sin 45^{\circ}} & \text { (15) } \frac{\sin 60^{\circ} \cos 70^{\circ}}{\tan 46^{\circ} \sin 30^{\circ}}\end{array} \)

**(1)** We use a calculator to find \[ \cos 23^\circ \approx 0.92. \] **(2)** \[ \sin 68^\circ \approx 0.93. \] **(3)** \[ \tan 64^\circ \approx 2.05. \] **(4)** \[ \cos 34^\circ \approx 0.83. \] **(5)** Since \(\cos 45^\circ \approx 0.7071\), \[ 2 \cos 45^\circ \approx 2 \times 0.7071 = 1.41. \] **(6)** With \(\sin 65^\circ \approx 0.9063\), \[ 5 \sin 65^\circ \approx 5 \times 0.9063 = 4.53. \] **(7)** Given \(\tan 58^\circ \approx 1.6003\), \[ 7 \tan 58^\circ \approx 7 \times 1.6003 = 11.20. \] **(8)** Since \(\sin 30^\circ = 0.5\), \[ -4 \sin 30^\circ \approx -4 \times 0.5 = -2.00. \] **(9)** With \(\sin 70^\circ \approx 0.9397\), \[ \frac{1}{3} \sin 70^\circ \approx \frac{1}{3} \times 0.9397 = 0.31. \] **(10)** Given \(\sin 60^\circ \approx 0.8660\), \[ \frac{\sin 60^\circ}{20} \approx \frac{0.8660}{20} = 0.04. \] **(11)** With \(\cos 24^\circ \approx 0.9135\), \[ \frac{\cos 24^\circ}{24} \approx \frac{0.9135}{24} = 0.04. \] **(12)** Calculate the angle sum first: \[ 54^\circ + 25^\circ = 79^\circ. \] Then, \[ \tan(79^\circ) \approx 5.14. \] **(13)** Using the calculator we find: \[ \tan 54^\circ \approx 1.38 \quad \text{and} \quad \tan 25^\circ \approx 0.46. \] So, \[ \tan 54^\circ + \tan 25^\circ \approx 1.38 + 0.46 = 1.84. \] **(14)** First, compute \(\sin 45^\circ \approx 0.7071\), then \[ -25 \sin 45^\circ \approx -25 \times 0.7071 = -17.68. \] Thus, \[ \frac{40}{-17.68} \approx -2.26. \] **(15)** We are given \[ \frac{\sin 60^\circ \cos 70^\circ}{\tan 46^\circ \sin 30^\circ}. \] Using approximate values: \[ \sin 60^\circ \approx 0.8660, \quad \cos 70^\circ \approx 0.3420, \quad \tan 46^\circ \approx 1.04, \quad \sin 30^\circ = 0.5. \] Compute the numerator: \[ 0.8660 \times 0.3420 \approx 0.2963. \] Compute the denominator: \[ 1.04 \times 0.5 = 0.52. \] Thus, \[ \frac{0.2963}{0.52} \approx 0.57. \] **Final Answers:** \[ \begin{array}{ll} (1) & 0.92, \\ (2) & 0.93, \\ (3) & 2.05, \\ (4) & 0.83, \\ (5) & 1.41, \\ (6) & 4.53, \\ (7) & 11.20, \\ (8) & -2.00, \\ (9) & 0.31, \\ (10) & 0.04, \\ (11) & 0.04, \\ (12) & 5.14, \\ (13) & 1.84, \\ (14) & -2.26, \\ (15) & 0.57. \end{array} \]