Fifp507 Fifp507
  • 21-07-2021
  • Mathematics
contestada

find csc theta and sin theta if tan theta = 7/4 and sin theta less than 0

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sqdancefan
sqdancefan sqdancefan
  • 03-08-2021

9514 1404 393

Answer:

  sin(θ) = (-7√65)/65

  csc(θ) = (-√65)/7

Step-by-step explanation:

The angle will have the given characteristics if its terminal ray passes through the 3rd-quadrant point (-4, -7). The distance from the origin to that point is ...

  d = √((-4)² +(-7)²) = √65

The sine of the angle is the ratio of the y-coordinate to this value:

  sin(θ) = -7/√65

  sin(θ) = (-7√65)/65

The cosecant is the inverse of the sine

  csc(θ) = (-√65)/7

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