Given sin(−θ)=−16 and tanθ=−35√35 .

what is the value of cosθ ?

- 16/(35√35)

Step-by-step explanation:

Recall that

sin(−θ)= -sin(θ) ===> sin(θ) = -sin(−θ)

and

tanθ = sinθ/cosθ ===> cosθ = sinθ/tanθ

With the data we have, then

cosθ = (-sin(−θ))/tanθ = -(-16)/(−35√35) = - 16/(35√35)

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is