SOLUTION: given tanθ = - 9/4, where 270°≤ θ ≤ 360°: a) state the other five trigonometric ratios as fractions - show all steps b determine the value of θ to the nearest degree - s

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Question 1201966: given tanθ = - 9/4, where 270°≤ θ ≤ 360°:
a) state the other five trigonometric ratios as fractions - show all steps
b determine the value of θ to the nearest degree - show all steps
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x represent theta.
tan(x) = -9/4 where 270 <= x <= 360.
draw the angle in the 4th quadrant.
vertex is at 0.
horizontal length = 4
vertical length = -9
hypotenuse = sqrt(4^2 + (-9)^2) = 9.848857802.
amgle x is equal to -66.03751103.
that's the negative angle in the fourth quadrant.
add 360 to that to get angle x = 293.962489 degrees.
that's the equivalent positive angle in the fourth quadrant.
the 6 trigonometric ratios are:
sine(x) = -9 / sqrt(97)
cosine(x) = 4 / sqrt((97)
tangent(x) = -9 / 4
cotangent(x) = 1/tangent(x) = 4 / -9
secant(x) = 1/cosine(x) = sqrt(97) / 4
cosecant(x) = 1/sine(x) = sqrt(97) / -9


Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
given tanθ = - 9/4, where 270°≤ θ ≤ 360°:
a) state the other five trigonometric ratios as fractions - show all steps
b determine the value of θ to the nearest degree - show all steps


Since tan θ = -+9%2F4, and 270° ≤ θ ≤ 360°, θ is in the 4th Quadrant, 
where sin, csc, tan and cotan are negative (< 0), while and cos and sec are positive (> 0). 
 
                

                                       

                        Therefore,    

                         There are your TRIG. RATIOS! You can now convert each to its nearest-degree measure!!