Find out the values of angles 120°, -135°, 150°, 180°, 270° for all the six trigonometric ratios.

We need to find out the values of angles 120°, -135°, 150°, 180°, 270° for all the six trigonometric ratios.

120 degrees

Given below is the value of 120º for all the trigonometric ratios

  • sin 120° = sin (1 × 90° + 30°) = cos 30° = √3/2
  • cos 120° = cos (1 × 90° + 30°) = – sin 30° = – 1/2
  • tan 120° = tan (1 × 90° + 30°) = – cot 30° = – √3
  • csc 120° = csc (1 × 90° + 30°) = sec 30° = 2/√3
  • sec 120° = sec (1 × 90° + 30°) = – csc 30° = – 2
  • cot 120° = cot (1 × 90° + 30°) = – tan 30° = – 1/√3

-135 degrees

Given below is the value of -135º for all the trigonometric ratios

  • sin (- 135°)= – sin 135°= – sin (1 × 90°+ 45°) = – cos 45° = – 1√2
  • cos (- 135°)= cos 135°= cos (1 × 90°+ 45°) = – sin 45°= – 1√2
  • tan (- 135°) = – tan 135° = – tan ( 1 × 90° + 45°) = – (- cot 45°) = 1
  • csc (- 135°)= – csc 135°= – csc (1 × 90°+ 45°)= – sec 45° = – √2
  • sec (- 135°)= sec 135°= sec (1 × 90°+ 45°)= – csc 45°= – √2
  • cot (- 135°) = – cot 135° = – cot ( 1 × 90° + 45°) = – (-tan 45°) = 1

150 degrees

Given below is the value of 150º for all the trigonometric ratios

  • sin 150° = sin (2 × 90° – 30°) = sin 30° = 1/2
  • cos 150° = cos (2 × 90° – 30°) = cos 30° = – √3/2
  • tan 150° tan (2 × 90° – 30°) = – tan 30° = – 1√3
  • csc 150° = csc (2 × 90° – 30°) = csc 30° = 2
  • sec 150° = sec (2 × 90° – 30°) = sec 30° = – 2√3
  • cot 150° = cot (2 × 90° – 30°) = – cot 300 = – √3

180 degrees

Given below is the value of 180º for all the trigonometric ratios

  • sin 180° = sin (2 × 90° – 0°) = sin 0° = 0
  • cos 180° = cos (2 × 90° – 0°) = – cos 0° = – 1
  • tan 180° = tan (2 × 90° + 0°) = tan 0° = 0
  • csc 180° = csc (2 × 90° – 0°) = csc 0° = Undefined
  • sec 180° = sec (2 × 90° – 0°) = – sec 0° = – 1
  • cot 180° = cot (2 × 90° + 0°) = cot 0° = Undefined

270 degrees

Given below is the value of 270º for all the trigonometric ratios

  • sin 270° = sin (3 × 90° + 0°) = – cos 0° = – 1
  • cos 270° = cos (3 × 90° + 0°) = sin 0° = 0
  • tan 270° = tan (3 × 90° + 0°) = – cot 0° = Undefined
  • csc 270° = csc (3 × 90° + 0°) = – sec 0° = – 1
  • sec 270° = sec (3 × 90° + 0°) = csc 0° = Undefined
  • cot 270° = cot (3 × 90° + 0°) = – tan 0° = 0

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