tentukan nilai trigonometri sudut berikut tanpa bantuan tabel dan kalkulator. a.sin 75° b.cos 195° c.cos 255° d.Tan 345°

a) sin 75°
[tex] = \sin \: ({30}^{0} + {45}^{0} ) \\ \\ = \sin \: {30}^{0} . \cos \: {45}^{0} + \cos \: {30}^{0} . \sin \: {45}^{0} \\ \\ = \frac{1}{2} \times \frac{ \sqrt{2} }{2} + \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{2} }{2} \\ \\ = \frac{ \sqrt{2} }{4} + \frac{ \sqrt{6} }{4} \\ \\ = \frac{ \sqrt{2} + \sqrt{6} }{4} [/tex]
b) cos 195⁰
[tex] = \cos( {225}^{0} - {30}^{0} ) \\ \\ = \cos {225}^{0} . \cos {30}^{0} + \sin{225}^{0} . \sin{30}^{0} \\ \\ = - \frac{ \sqrt{2} }{2} \times \frac{ \sqrt{3} }{2} - \frac{ \sqrt{2} }{2} \times \frac{1}{2} \\ \\ = - \frac{ \sqrt{6} }{4} - \frac{ \sqrt{2} }{4} \\ \\ = - ( \frac{ \sqrt{6} + \sqrt{2} }{4} ) \\ \\ = - \frac{ \sqrt{6 } + \sqrt{2} }{4} [/tex]
c) cos 225⁰
[tex] = - \frac{ \sqrt{2} }{2 } \\ [/tex]
4) tan 345⁰
[tex] = \tan( {165}^{0} + {180}^{0} ) \\ \\ = \tan{165}^{0} \\ \\ = \tan( {30}^{0} + {135}^{0} ) \\ \\ = \frac{ \tan {30}^{0} + \tan{135}^{0} }{1 - \tan{30}^{0}. \tan {135}^{0} } \\ \\ = \frac{ \frac{ \sqrt{3} }{3} - 1}{1 - \frac{ \sqrt{3} }{3} ( - 1)} \\ \\ = \frac{ \frac{ \sqrt{3} - 3 }{3} }{1 + \frac{ \sqrt{3} }{3} } \\ \\ = \frac{ \sqrt{3} - 3 }{3 + \sqrt{3} } \\ \\ = \frac{( \sqrt{3} - 3)(3 - \sqrt{3} ) }{6} \\ \\ = \frac{3 \sqrt{3} - 3 - 9 + 3 \sqrt{3} }{6} \\ \\ = \frac{6 \sqrt{3} - 12}{6} \\ \\ = \frac{6( \sqrt{3} - 2) }{6} \\ \\ = \sqrt{3} - 2[/tex]