Question

Use inverse trigonometric functions to solve the following equations. If there is more than one solution, enter all solutions as a comma-separated list (like "1, 3"). If an equation has no solutions, enter "DNE".Solve 6sin(θ)=1 for θ (where 0≤θ<2π).θ=Solve 9sin(θ)=9 for θ (where 0≤θ<2pi).θ=Solve 5sin(θ)=13 for θ (where 0≤θ<2π).θ=

Answer 1

We have to apply the inverse trigonometric functions to solve this equations:

a)

$\begin{gathered} 6\sin (\theta)=1 \\ \sin (\theta)=\frac{1}{6} \\ \theta=\arcsin (\frac{1}{6}) \\ \theta_1\approx0.167 \\ \theta_2=\pi-0.167\approx2.974 \end{gathered}$

b)

$\begin{gathered} 9\cdot\sin (\theta)=9 \\ \sin (\theta)=1 \\ \theta=\arcsin (1)=\frac{\pi}{2}\approx1.571 \end{gathered}$

c)

$\begin{gathered} 5\cdot\sin (\theta)=13 \\ \sin (\theta)=\frac{13}{5} \\ \theta=\arcsin (\frac{13}{5})\longrightarrow\text{ no solution} \end{gathered}$

Answer:

a) θ = 0.167, 2.974

b) θ = 1.571

c) θ = DNE