g the value of tan(-150) is because -150 is in quadrant the reference angle is and the exact value of tan (-150) is

Step-by-step explanation:

Given the expression tan (-150), from trigonometry identity, tan(-θ) = -tanθ

Hence  tan (-150) = - tan 150

First is to find the value of tan 150.

tan 150 = tan (180-30)

tan (A+B) = (tan180 - tan30)/1+tan180tan30

tan (180-30) = (0 - 1/√3)/1+0(1/√3)

tan (180-30) =  -1/√3/1

tan (180-30) =  -1/√3

Since tan 150 =   -1/√3

-tan 150 = -(- 1/√3)

-tan 150 =   1/√3

Since -tan 150 = tan (-150) =  1/√3

Hence the exact value of tan (-150) is   1/√3

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).