Answer:
Cosec θ = – 25/24
Explanation:
From the question given, we obtained the following information:
Tan θ = – 24/7
Cosec θ =?
Tan θ is negative in the forth quadrant.
Please see attached photo.
Tan θ = Opposite /Adjacent
Opposite = – 24
Adjacent = 7
Hypothenus = x
Thus, we can obtain the value of x by using the pythagoras theory as illustrated below:
x² = (–24)² + 7²
x² = 576 + 49
x² = 625
Take the square root of both side
x = √625
x = 25
Next, we shall determine Sine θ. This can be obtained as follow:
Opposite = – 24
Hypothenus = 25
Sine θ = ?
Sine θ = Opposite /Hypothenus
Sine θ = –24/25
Finally, we shall determine the Cosec θ. This can be obtained as follow:
Cosec θ = 1 /Sine θ
Sine θ = –24/25
Cosec θ = 1 ÷ –24/25
Cosec θ = 1 × – 25/24
Cosec θ = – 25/24