Solving trigonometric equations assignment

The motion of a weight that hangs from a spring is represented by the equation h = 8sin( 2pi/3 t). It models the weight's height (in inches) above or below the rest position as a function of time (in seconds). Approximately when will the object be 3 inches above the rest position? Round to the nearest hundredth.

0.18 seconds

Solve 2sec(x) + 5 = 9 Which equation is equivalent to the given equation? Which are solutions to the given equation?

[A] cos(x) = 1/2 [A] pi/3 +2kpi and 5pi/3 + 2kpi

Solve: tan(x) - cos^2(x) = sin^2(x)

[A] pi/4 + kpi

Select all of the following that represent the exact solutions of sin(x) = sqrt3/2 Evaluate sin^-1(1)

pi/3 + 2kpi 2pi/3 + 2kpi pi/2

Remember the definition of csc(x) To graph y = csc^-1(X) on the calculator, which expression should be typed in the calculator? What is the range of y = csc^1(x)?

y = sin^-1(1/x) [ -pi/2,0 ) and ( 0, pi/2 ]

Does the equation sin2(x) - 4 = 0 have any solutions? Explain.

Isolate sin(x) by adding 4 and taking the square root of both sides.State that sin(x) = 2 or sin(x) = -2.State that -2 and 2 are undefined values of the inverse sine function. There are no solutions because -2 and 2 are not in the domain of the function.

Solve 2sin^2(x) - 5sin(x) - 3 = 0. Let u = sin(x) Which of the following is equivalent to the given equation? What are the solutions to the equation?

[A] (2u + 1)(u - 3) = 0 7pi/6 + 2kpi 11pi/6 + 2kpi

Which is the graph of the inverse secant function?

[A] the first graph

Solve: 2cos(x) + sqrt2 = 0 for 0 <= x <= 2pi Chech all that apply.

3pi/4 5pi/4