Solve, for 0 ≤ θ < 360 , the equation
sin2 θ = 1 + cos θ

θ = 90°, 180°, or 270°

Step-by-step explanation:

sin²θ = 1 + cos θ

Use Pythagorean identity.

1 − cos²θ = 1 + cos θ

Move everything to one side and simplify.

0 = cos²θ + cos θ

Factor.

0 = cos θ (cos θ + 1)

Solve.

cos θ = 0 or -1

θ = 90°, 180°, or 270°

answer: given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

therefore, it will take you 12.94 minutes to get to the front of the line.

step-by-step explanation:

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