Trigonometric Equations

Disclaimer: The material in the videos below comes mainly from outside City Tech. The presentation in these videos may differ from the one given in your class. Please consult with your instructor to confirm whether a particular approach is acceptable in your class.

  1. $\rhd$ Solving sinusoidal equations of the form sin(x)=d (6:10) Sal finds the expressions that together give all solutions to the equation $\sin(x) = \dfrac{1}{3}$.
  2. $\rhd$ Solving cos(x)=1 and cos(x)=-1 (5:18) Solving $\cos(\theta) = 1$ and $\cos(\theta) = -1$ using the graph of $\cos(x)$. (5:18)
  3. * Practice: Solve equations like $\sin(x) = d$ or $\cos(x) = d$ where $d$ is any number. (4 problems)
  4. * Practice: Solve equations of the type $a \cdot\sin(bx+c) = d$ or  $a \cdot \cos(bx+c) = d$. (4 problems)
  5. $\rhd$ Solve trigonometric equation (8:11) Solve $2\sin^2(x)=\sin(x)$
  6. $\rhd$ Solving Trigonometric Equations By Finding All Solutions (11:49) Solve $\sin(x)=\frac 1 2$, and $\cos(x)=-\frac{\sqrt{2}}2$, and $2\sin(x)+\sqrt{3}=0$, and $3\tan(x)+\sqrt{3}=0$, and $2\sin^2(x)-1=0$
  7. $\rhd$ Solving Trigonometric Equations By Factoring & By Using Double Angle Identities (18:31) Solve, for example, $\sin^2x+2\sin x-3=0$, and $2\cos^2 x-\cos x-3=0$, and $4\sin^2 x-1=0$