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Answer:
- sin(θ) = -7/√65
- csc(θ)=-√65/7
- cot=-4/7
Explanation:
For the sine (and cosecant) function, we need to know the distance from the origin to the given point. The distance formula works for that.
d = √(4² +(-7)²) = √(16 +49) = √65
The sine is the ratio y/d; the cosecant is the inverse of the sine. The cotangent is the ratio x/y.
sin(θ) = y/d = -7/√65
csc(θ) = 1/sin(θ) = -√65/7
cot(θ) = x/y = -4/7
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If you need to have the denominator be rational for the sine, then multiply by √65/√65 to get sin(θ) = (-7/65)√65.