Hurry i need (15 points)
solve sinø+1=cos2ø on the interval 0≤ø< 2π

0, π, 7π/6, 11π/6   on the interval 0 ≤ ø <2π.

Step-by-step explanation:

sinø + 1 = cos2ø

Use the identity cos 2o = 1 - 2 sin^2 o:

sin o + 1 = 1 - 2 sin^2 o

2sin^2 o + sin o + 1 - 1 = 0

2 sin^2 o + sin o = 0

sin o (2 sin 0 + 1) = 0

Therefore sin o = 0 or sin o = -1/2.

For sin o = 0 , o = 0, π radians.

For sin o = - 1/2, o = 7π/6, 11π/6 radians.

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