Solving Trigonometric Equations

What is the sine double angle identity?

• @@ ext{sin}(2x) = 2 ext{sin}(x) ext{cos}(x)@@

• @@ ext{sin}(2x) = ext{sin}(x) + ext{cos}(x)@@

• @@ ext{sin}(2x) = 2 ext{sin}(x) - 2 ext{cos}(x)@@

• @@ ext{sin}(2x) = ext{sin}^2(x) + ext{cos}^2(x)@@

How do you solve @@50\text{sin}^2x = 50 + 75\text{sin}x@@?

• Rearrange to form a quadratic equation in terms of @@\text{sin}x@@: @@50\text{sin}^2x - 75\text{sin}x - 50 = 0@@. Use the quadratic formula to find @@\text{sin}x@@, then solve for @@x@@.

• Use trigonometric identities to simplify the equation and find @@x@@ directly.

• Graph the function and find the intersection points with the x-axis.

• Differentiate the equation and find the critical points.

What is the cosine double angle identity?

• @@ ext{cos}(2x) = ext{cos}^2(x) - ext{sin}^2(x)@@

• @@ ext{cos}(2x) = ext{sin}^2(x) - ext{cos}^2(x)@@

• @@ ext{cos}(2x) = 2 ext{sin}^2(x) - 1@@

• @@ ext{cos}(2x) = 2 ext{cos}^2(x) - 1@@

What is the solution set for the equation @@( ext{cos}\, x - 1)(2 ext{sin}\, x + 1) = 0@@ in the interval @@(0, 2 ext{pi}]@@?

• @@ ext{2 ext{pi}, } rac{7 ext{pi}}{6}, rac{11 ext{pi}}{6}@@

• @@rac{ ext{pi}}{3}, rac{5 ext{pi}}{3}, ext{0}@@

• @@rac{ ext{pi}}{2}, rac{3 ext{pi}}{2}, ext{0}@@

• @@rac{5 ext{pi}}{6}, rac{7 ext{pi}}{6}, rac{11 ext{pi}}{6}@@

What is the tangent function's periodicity?

• @@2 ext{pi}@@

• @@ ext{pi}@@

• @@rac{ ext{pi}}{2}@@

• @@ ext{pi}^2@@

What are the solutions for @@50\text{sin}^2x = 50 + 75\text{sin}x@@ in the interval @@(0, 2\text{pi}]@@?

• @@\frac{7\text{pi}}{6}@@

• @@\frac{11\text{pi}}{6}@@

• @@\frac{\text{pi}}{3}@@

• @@\frac{5\text{pi}}{6}@@

What is a trigonometric equation?

• An equation that involves trigonometric functions of a variable, typically an angle.

• A type of equation that only includes linear terms.

• An equation that can only be solved graphically.

• A polynomial equation with no trigonometric functions.

What is the periodicity of the cosine function?

• @@rac{2 ext{pi}}{3}@@

• @@ ext{pi}@@

• @@2 ext{pi}@@

• @@4 ext{pi}@@

What are the solutions for @@2\text{sin}\, x \tan x + 2\text{sin}\, x = 0@@ in the interval @@(0, 2\text{pi}]@@?

• @@\frac{3\text{pi}}{4}@@

• @@\frac{5\text{pi}}{4}@@

• @@\text{pi}@@

• @@\frac{7\text{pi}}{4}@@

• @@2\text{pi}@@

What is the periodicity of the sine function?

• @@rac{2 ext{pi}}{3}@@

• @@2 ext{pi}@@

• @@ ext{pi}@@

• @@4 ext{pi}@@