If tan theta equals 15/8 in quadrant 3 and you need to find the sin, cos, and tan of double angle, in what quadrant would the double angle reside.

sin2θ = 240/289

             cos2θ = -161/289

             tan2θ = -240/161

              2θ is in quadrant 2

Step-by-step explanation: tanθ = 15/8

sinθ/cosθ = 15/8

sinθ = 15cosθ/8

sin²θ + cos²θ = 1

(15cosθ/8)² + cos²θ = 1

225cos²θ/64 + cos²θ = 1

225cos²θ + 64cos²θ = 64

289cos²θ = 64

cos²θ = 64/289

cosθ = ±√64/289

cosθ = ±8/17

As tanθ in quad 3 ⇒ tanθ is +, cosθ is - and sinθ is -

So, cosθ = -8/17

as sin θ = 15cosθ/8 = -15/17

For sin2θ = 2sinθcosθ = 2.(-15/17).(-8/17) = 240/289

For cos2θ = cos²θ - sin²θ = (-8/17)² - (-15/17)² = -161/289

For tan2θ = sin2θ/cos2θ = (240/289) / (-161/289) = -240/161

As sin2θ + and cos2θ - ⇒ 2θ is in quadrant 2

y=mx+b

step-by-step explanation:

m slope

b y-intercept

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional