Given:
csc = - 17/15 where 270 < 360
cot = -3/4 where 90 < 180
Find the exact value of sin. Show all work.
You say 270 is less than 360 and 90 is
less than 180. That is quite ovious.
Please clarify your problem.
To find the exact value of sine (sin), we can use the identity:
sin^2θ + cos^2θ = 1
Given that csc (cosecant) is the reciprocal of sin, we can write:
csc^2θ = 1/sin^2θ
Solving for sin^2θ:
1/sin^2θ = (csc^2θ)^-1
1/sin^2θ = (-17/15)^-1
Now, take the reciprocal:
sin^2θ = (15/-17)^-1
To find sinθ, we take the square root of sin^2θ:
sinθ = ±√[(15/-17)^-1]
Since the original problem doesn't specify the range of θ, we consider both positive and negative solutions.
Let's evaluate the expression:
sinθ = ±√[(15/-17)^-1]
= ±√(-17/15)
= ±(√(-17)/√15) (Breaking down the square root of a fraction)
At this point, we encounter a problem. The square root of a negative number is not a real number within the real number system. Therefore, there is no exact value for sinθ given the conditions provided.
Please note that if the range of θ was outside the given range (270° < θ < 360°), it may be possible to find a real solution.
If you have a different range for θ or if there is additional information, please provide it, so we can help you further.