If tan Ф = 15/8 then we have these trigonometric functions cosec Ф = 17/15, sec Ф = 17/8 and cot Ф = 8/15.
According to the question,
We have the following information:
Tan Ф = 15/8
We know that in this trigonometric function we have perpendicular divided by base.
Now, we can find the hypotenuse using the Pythagoras theorem:
Let's denote hypotenuse with h, perpendicular with p and base with b.
[tex]h^{2} =p^{2} +b^{2}[/tex]
[tex]h^{2}[/tex] = [tex](15)^{2} +(8)^{2}[/tex]
[tex]h^{2} = 225+64\\h^{2} = 289\\h = \sqrt{289}[/tex]
h = 17 units
Now, we have the following values:
Cosec Ф = 17/15 (Hypotenuse/perpendicular)
Sec Ф = 17/8 (h/b)
Cos Ф = 8/17 (b/h)
Cot Ф = 8/15 (b/p)
Hence, the correct options are A, B and D.
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