# Calculate the sines, cosines and tangents of the angles 120, 135 and 150 degrees.

1) Calculate the sines of these angles equal to 120 °, 135 ° and 150 ° using the reduction formula sin (90 ° + x) = cos (x):
sin (120 °) = sin (90 ° + 30 °) = cos (30 °) = √3 / 2;
sin (135 °) = sin (90 ° + 45 °) = cos (45 °) = √2 / 2;
sin (150 °) = sin (90 ° + 60 °) = cos (60 °) = 1/2.
2) Calculate the cosines of these angles equal to 120 °, 135 ° and 150 °, using the reduction formula cos (90 ° + x) = – sin (x):
cos (120 °) = cos (90 ° + 30 °) = – sin (30 °) = – 1/2;
cos (135 °) = cos (90 ° + 45 °) = – sin (45 °) = – √2 / 2;
cos (150 °) = cos (90 ° + 60 °) = – sin (60 °) = – √3 / 2.
3) Since tg (x) = sin (x) / cos (x), then:
tg (120 °) = sin (120 °) / cos (120 °) = (√3 / 2) / (- 1/2) = (√3 / 2) * (- 2/1) = – √3;
tg (135 °) = sin (135 °) / cos (135 °) = (√2 / 2) / (- √2 / 2) = – 1;
tg (150 °) = sin (150 °) / cos (150 °) = (1/2) / (- √3 / 2) = (1/2) * (- 2 / √3) = – 1 / √ 3 = -√3 / 3.

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