Determine approximate solutions for each equation in the interval x\in [0, 2\pi] to the nearest hundredth of a radian.

\displaystyle \sin x -\frac{1}{4} = 0

Determine approximate solutions for each equation in the interval x\in [0, 2\pi] to the nearest hundredth of a radian.

\displaystyle \cos x +\frac{3}{4} = 0

Determine approximate solutions for each equation in the interval x\in [0, 2\pi] to the nearest hundredth of a radian.

\displaystyle \tan x - 5= 0

Determine approximate solutions for each equation in the interval x\in [0, 2\pi] to the nearest hundredth of a radian.

\displaystyle \sec x - 4= 0

Determine approximate solutions for each equation in the interval x\in [0, 2\pi] to the nearest hundredth of a radian.

\displaystyle 3\cot x + 2= 0

Determine approximate solutions for each equation in the interval x\in [0, 2\pi] to the nearest hundredth of a radian.

\displaystyle 2\csc x + 5= 0

Determine exact solutions for each equation in the interval x\in [0, 2\pi].

\displaystyle \sin x + \frac{\sqrt{3}}{2} = 0

Determine exact solutions for each equation in the interval x\in [0, 2\pi].

\displaystyle \cos x - 0.5 = 0

Determine exact solutions for each equation in the interval x\in [0, 2\pi].

\displaystyle \tan x - 1= 0

Determine exact solutions for each equation in the interval x\in [0, 2\pi].

\displaystyle \cot x + 1= 0

Determine approximate solutions for each equation in the interval x\in [0, 2\pi], to the nearest hundredth of a radian.

\sin^2x -0.64 = 0

Determine approximate solutions for each equation in the interval x\in [0, 2\pi], to the nearest hundredth of a radian.

\cos^2x -\frac{4}{9} = 0

Determine approximate solutions for each equation in the interval x\in [0, 2\pi], to the nearest hundredth of a radian.

\tan^2x -1.44 = 0

Determine approximate solutions for each equation in the interval x\in [0, 2\pi], to the nearest hundredth of a radian.

\sec^2x -2.5 = 0

Determine approximate solutions for each equation in the interval x\in [0, 2\pi], to the nearest hundredth of a radian.

\cot^2x -1.21 = 0

Determine exact solutions for each equation in the interval x\in [0, 2\pi].

\displaystyle \sin^2x - \frac{1}{4} = 0

Determine exact solutions for each equation in the interval x\in [0, 2\pi].

\displaystyle \cos^2x - \frac{3}{4} = 0

Determine exact solutions for each equation in the interval x\in [0, 2\pi].

\displaystyle \tan^2x - 3 = 0

Determine exact solutions for each equation in the interval x\in [0, 2\pi].

\displaystyle 3\csc^2x - 4 = 0

Solve \sin^2x - 2\sin x - 3 =0 on the interval x\in [0, 2\pi].

Solve \csc^2x - \csc x - 2 =0 on the interval x\in [0, 2\pi].

Solve 2\sec^2x + \sec x - 1 =0 on the interval x\in [0, 2\pi].

Solve \tan^2x + \tan x - 6 =0 on the interval x\in [0, 2\pi]. Round answers to the nearest hundredth o a radian.

Determine approximate solutions for each equation in the interval 2x \in [0, \pi], to the nearest hundredth of a radian.

\sin 2x - 0.8 = 0

Determine approximate solutions for each equation in the interval 2x \in [0, \pi], to the nearest hundredth of a radian.

5\sin 2x - 3 = 0

Determine approximate solutions for each equation in the interval 2x \in [0, \pi], to the nearest hundredth of a radian.

-4\sin 2x + 3 = 0

Solve 2\tan^2x + 1 = 0 on the interval x\in [0, 2\pi].

Solve 3\sin 2x - 1 = 0 on the interval x\in [0, 2\pi].

Solve 6\cos^2x - 5\cos x - 6 = 0 on the interval x\in [0, 2\pi].

Solve 3\csc^2x - 5\csc x -2 = 0 on the interval x\in [0, 2\pi].

Solve \sec^2x + 5\sec x + 6 = 0 on the interval x\in [0, 2\pi].

Solve 2\tan^2x - 5\sec x -3 = 0 on the interval x\in [0, 2\pi].

Consider the trigonometric equation 3\sin^2x + \sin x - 1 = 0.

• Explain why the left side of the equation cannot be factored.

Consider the trigonometric equation 3\sin^2x + \sin x - 1 = 0.

Use the quadratic formula to obtain the roots.

Consider the trigonometric equation 3\sin^2x + \sin x - 1 = 0.

Determine all solutions in the interval x \in [0, 2\pi].

The height, h, in metres, above the ground of a rider on a Ferris wheel can be modelled by the equation h = 10\sin(\frac{\pi}{12}(t - 7.5)) + 12, where t is the time, in seconds.

At t = 0 s, the rider is at the lowest point. Determine the first two times that the rider is 20 m above the ground, to the nearest hundredth of a second.

Consider the trigonometric equation 4\sin x \cos 2x + 4\cos x \sin 2x - 1 = 0 in there interval x \in [0, 2\pi]. Either show that there is no solution to the equation in this domain, or determine the smallest possible solution.

Consider the equation 2\cos^2x + \sin x - 1= 0.

Explain why the equation cannot be factored.

Consider the equation 2\cos^2x + \sin x - 1= 0.

Suggest a trigonometric identity that can be used to factor.

Consider the equation 2\cos^2x + \sin x - 1= 0.

i) Apply the identity and rearrange the equation into a factorable form.

ii) Factor the equation.

iii) Determine all solutions in the interval x \in [0, 2\pi].

Determine solutions for \tan x \cos^2x -\tan x = 0 in the interval x \in [-2\pi, 2\pi].

The voltage, V, in volts, applied to an electric circuit can be modelled by the equation V = 167 \sin(120\pi t), where t is the time, in seconds. A component in the circuit can be safely withstand a voltage of more than 120 V for 0.01 s or less.

Determine the length of time that the voltage is greater than 120 V on each half-cycle.

The voltage, V, in volts, applied to an electric circuit can be modelled by the equation V = 167 \sin(120\pi t), where t is the time, in seconds. A component in the circuit can be safely withstand a voltage of more than120 V for 0.01 s or less.

Is it safe to sue this component in this circuit? Just icy your answer.

Determine solutions for

\displaystyle \frac{\cos x}{1 +\sin x} + \frac{1 + \sin x}{\cos x} = 2

in the interval x \in [-2\pi, 2\pi].