Cosθ=−2√3 , where π≤θ≤3π2 .

tanβ=43 , where 0≤β≤π2 .

What is the exact value of sin(θ+β) ?

Enter your answer, as a fraction in simplified form, in the box.
sin(θ+β) =

Step-by-step explanation:

step 1

Find the  

we know that

Applying the trigonometric identity

we have

substitute

Remember that

π≤θ≤3π/2

so

Angle θ belong to the III Quadrant

That means ----> The sin(θ) is negative

step 2

Find the sec(β)

Applying the trigonometric identity

we have

substitute

we know

0≤β≤π/2 ----> II Quadrant

so

sec(β), sin(β) and cos(β) are positive

Remember that

therefore

step 3

Find the sin(β)

we know that

we have

substitute

therefore

step 4

Find sin(θ+β)

we know that

so

In this problem

we have

substitute the given values in the formula

bottom left

step-by-step explanation:

the x's and the y's both go up the same amount each time, therefore it will be a linear function because it will go in a straight line when drawn on a graph.

hope this !

is only a line? i think so