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

User Tyddlywink
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Answer:

sin(θ) = (-7√65)/65

csc(θ) = (-√65)/7

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

User Pbhd
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