MATHEMATICS
MORE EXERCISES
Special angles.

In this exercise calculators may
not be used.

Question  1
Write each of the following as the ratio of an acute
angle and hence determine the function value :

1.1  sin 150°                     [ A 1.1 ]
1.2  cos 210°                     [ A 1.2 ]
1.3  tan 135°                     [ A 1.3 ]
1.4  sec 150°                     [ A 1.4 ]
1.5  cosec 315°                 [ A 1.5 ]
1.6  cot 240°                     [ A 1.6 ]
1.7  cos 225°                     [ A 1.7 ]
1.8  cosec 120°                 [ A 1.8 ]
1.9  cot 135°                     [ A 1.9 ]
1.10  sin 330°                   [ A 1.10 ]
1.11  cos 210°                   [ A 1.11 ]
1.12  sec 300°                   [ A 1.12 ]
1.13  cos 120°                   [ A 1.13 ]
1.14  tan 210°                   [ A 1.14 ]
1.15  sin 225°                 [ A 1.15 ]
1.16  cos 315°                   [ A 1.16 ]
1.17  sin 300°                   [ A 1.17 ]
1.18  cos 120°                   [ A 1.18 ]
1.19  tan 120°                   [ A 1.19 ]
1.20  tan 225°                   [ A 1.20 ]

Question  2
Evaluate :

$$\hspace*{2 mm}\mathrm{2.1\kern3mm\sin\ 30°\ \bold{.}\ cos\ 60°\ \bold{.}\ cot\ 45°\kern2mm\ }$$          [ A 2.1 ]

$$\hspace*{2 mm}\mathrm{2.2\kern3mm\sec\ 30°\ \bold{.}\ cos\ 30°\ \bold{.}\ tan\ 60°\kern2mm\ }$$        [ A 2.2 ]

$$\hspace*{2 mm}\mathrm{2.3\kern3mm\ 4 \bold{.}\ sin\ 60°\ + tan\ 45°\ +\ 2 \bold{.}\ cot\ 30°\kern2mm\ }$$
[ A 2.3 ]

$$\hspace*{2 mm}\mathrm{2.4\kern3mm\sec^2\ 0°\ +\ cos^2\ 30°\ +\ cosec^2\ 45°\kern2mm\ }$$
[ A 2.4 ]

$$\hspace*{2 mm}\mathrm{2.5\kern3mm\frac{cosec\ 120°\ \bold{.}\ tan\ 135°\ \bold{.}\ sin\ 150°}{sec\ 150°}\kern2mm\ }$$
[ A 2.5 ]

$$\hspace*{2 mm}\mathrm{2.6\kern3mm\frac{−\ sin\ 120°\ \bold{.}\ cos\ 150°\ + sec^2\ 135°\ −\ cos\ 0°}{sin^2\ 135°\ \bold{.}\ cosec\ 135°}\kern2mm\ }$$

[ A 2.6 ]

$$\hspace*{2 mm}\mathrm{2.7\kern3mm\frac{cos\ 240°\ \bold{.}\ sin\ 330°\ \bold{.}\ tan\ 120°}{sin\ 150°\ \bold{.}\ tan\ 210° \bold{.}\ cos\ 120°}\kern2mm\ }$$

[ A 2.7 ]

$$\hspace*{2 mm}\mathrm{2.8\kern3mm\frac{sin\ 150°\ \bold{.}\ cos\ 225°\ \bold{.}\ sec\ 10°}{cosec\ 330°\ \bold{.}\ cosec\ 45° \bold{.}\ cosec\ 260°}\kern2mm\ }$$

[ A 2.8 ]

$$\hspace*{2 mm}\mathrm{2.9\kern3mm\frac{sin\ 150°\ \bold{.}\ cos\ 210°}{tan\ 330°}\kern2mm\ }$$                     [ A 2.9 ]

$$\hspace*{2 mm}\mathrm{2.10\kern3mm\frac{sin\ 210°\ \bold{.}\ cos\ 300°\ \bold{.}\ cot\ 150°}{cos\ 120°\ \bold{.}\ cot\ 240° \bold{.}\ sin\ 330°}\kern2mm\ }$$

[ A 2.10 ]

$$\hspace*{2 mm}\mathrm{2.11\kern3mm\frac{4}{3}cos^2\ 330°\ −\ \frac{1}{2}\ sec^2\ 45°\ −\ \frac{1}{3}\ sin\ 60°\kern2mm\ }$$

[ A 2.11 ]