SOLUTION: Given tan θ = -9/4, where 270° ≤ θ ≤ 360°, a) state the other five trigonometric ratios as fractions. b) determine the value of θ to the nearest degree I need steps p

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Question 1159432: Given tan θ = -9/4, where 270° ≤ θ ≤ 360°,
a) state the other five trigonometric ratios as fractions.
b) determine the value of θ to the nearest degree
I need steps please
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Given tan%28theta%29+=+-9%2F4, where 270+%3C=+theta+%3C=+360°,

a) state the other five trigonometric ratios as fractions.

if tan%28theta%29+=+-9%2F4,

since tan%28theta%29+=+y%2Fx, then y=-9 and x=4

then hypotenuse sqrt%284%5E2=%28-9%29%5E2%29=sqrt%2816%2B81%29=sqrt%2897%29

sin%28theta%29=-9%2Fsqrt%2897%29
cos%28theta%29=4%2Fsqrt%2897%29

b) determine the value of theta to the nearest degree
since in quadrant III, because given 270+%3C=+theta+%3C=+360°
theta=270-sin%5E-1%289%2Fsqrt%2897%29%29=270-%28-66.04%29=270%2B66.04=293.96=294°
theta=360-cos%5E-1%284%2Fsqrt%2897%29%29=360-66.04=294°
theta=360-tan%5E-1%28-9%2F4%29=360-66.04=294°

so, your angle is: theta=294°