Introduction to Solving Trig Equation with a linear equation with Trig example
Trig Equation in Quadratic Equation Form Differences of Squares
When the solution to Trig equation is not a special angle
Solving Trig Equation in ax^2+bx+c=0 form
Solving Trig Equation by Converting to Quadratic Equation form using Trig Identity
Solving Trig equation with Double Angles
Solving Trig Equation with a Phase Shift
Trig Equation with csc ratio and in Quadratic Form
Solving Trig Equation by simplifying it first using Double Angle Formula
Solving Trig Equation advanced example with sum of power of 6 of sin and cosine
Solving Trig Formula that requires simplification using Compounded Angle Formula
Solving Trig Equation in the form of A\sin x + B\cos x = C
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.
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].