IB Mathematics Analysis and Approaches SL 3.8—solving Trig Equations Questionbank

Show that the equation may be written as $6\cos^2x+\sin x-4=0.$

Express $\cos^2x$ in terms of $\sin x$, and hence obtain a quadratic equation in $\sin x$.

Solve $6\sin^2x-\sin x-2=0$ exactly for $\sin x$.

Determine all exact values of $x$ in the interval $0\le x<2\pi$ that satisfy the original equation.

Sketch the graphs of $y=3\cos(2x)$ and $y=1-\sin x$ for $0$, indicating approximate intersections matching the solutions from part 4.

Show that the equation may be written as $2\cos^2 x-\cos x-1=0$.

Factor the left-hand side to obtain an equation of the form $(2\cos x+1)(\cos x-1)=0$.

Find all exact values of $x$ in the interval $0\le x<2\pi$ that satisfy the equation.

Show that the equation may be written as $\cos^2 x+\frac{3}{2}\sin x=0$.

Express $\cos^2 x$ in terms of $\sin x$, and hence obtain a quadratic equation in $\sin x$.

Solve $2\sin^2 x-3\sin x-2=0$ exactly for $\sin x$.

Determine all exact values of $x$ in the interval $0\le x<2\pi$ that satisfy the original equation.

Show that the equation may be written as $4\cos^2x+1-3\sin x=0.$

Express $\cos^2x$ in terms of $\sin x$ and obtain a quadratic equation in $\sin x$.

Solve $4\sin^2x+3\sin x-5=0$ exactly for $\sin x$.

Determine all exact values of $x$ in the interval $0\le x<2\pi$ that satisfy the original equation.