Solve: sin(11pi/2 +x) =-1/2 for [pi, 2pi]

Step-by-step explanation:

Given the expression  sin(11pi/2 +x) =-1/2

Take the arcsin of both sides

sin⁻¹[sin(11pi/2 +x)] =sin⁻¹(-1/2)

11pi/2 + x = -30

x = -pi/6 - 11pi/2

Find the LCM

x = (-pi-33pi)/6

x = -34pi/6

x = -17pi/3

Since x is negative and sin is negative in the fourth quadrant

x =  - 17pi/2

x = -1530⁰+1440⁰ (scaling down the angle)

x = -90

x = 360 - 90 (fourth quadrant)

x = 270⁰

x = 270pi/180

x = 27pi/18

x = 3pi/2

Hence x the solution of x is 3pi/2

(x, y)→(x − 8, y − 7)

step-by-step explanation:

enjoy!

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: