Given that tan theta = -9/4, where 270° ≤ theta ≤ 360° a)state the 5 trigonometric ratios as a fraction b) determine the value of theta to the nearest degree

Step-by-step explanation:

θ lies in 4th quadrant.

cos θ and sec θ are positive all other trigonometric ratios are negative.

sin θ/cos θ=-9/4

sin θ=-9/4 cos θ

we know sin² θ +cos ² θ =1

(-9/4 cos θ)²+cos ² θ =1

cos ²  θ (81/16+1)=1

cos ²θ((81+16)/16)=1

cos² θ=16/97

cos θ=4/√97

sin θ=-9/4*4/√97=-9/√97

sec θ=1/cos θ=√97/4

cosec θ=1/sin θ=-√97/9

cot θ=1/tan θ=-4/9

4444444444444 i think

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.