Trigonometry and Quadratic Equations Quiz

The video tutorial addresses a trigonometric problem submitted by a viewer named Bradley. The problem involves solving the equation 3 sine squared of x equals 1 plus cosine of x. The instructor explains the use of trigonometric identities to simplify the equation and transform it into a quadratic equation. By substituting variables, the quadratic equation is solved using the quadratic formula. The solutions are verified, and the instructor concludes by thanking Bradley for the interesting problem.

What was the initial problem presented in the video?

• 2 sine x equals cosine x

• 3 cosine squared of x equals 1 plus sine of x

• 3 sine squared of x equals 1 plus cosine of x

• sine x equals cosine x

Which trigonometric identity is used to simplify the equation?

• sine squared x plus cosine squared x equals 1

• sine x equals cosine x

• tangent x equals sine x over cosine x

• cosine squared x minus sine squared x equals 1

What substitution is made to transform the equation into a quadratic form?

• a equals sine of x

• b equals tangent of x

• d equals cosine of x

• c equals cosine of x

What is the quadratic equation derived from the trigonometric equation?

• 3a squared minus a plus 2 equals 0

• a squared plus 2a minus 3 equals 0

• 2a squared plus 3a minus 1 equals 0

• 3a squared plus a minus 2 equals 0

What are the solutions to the quadratic equation?

• a equals -1 and 2/3

• a equals 1 and 2/3

• a equals 1 and -2/3

• a equals -1 and -2/3

What is the value of x when cosine of x equals -1?

• x equals 2pi

• x equals pi/2

• x equals 0

• x equals pi

What tool is suggested to find the arccosine of 2/3?

• A trigonometry table

• A scientific calculator

• A graphing calculator

• Google

What is the approximate value of x when cosine of x equals 2/3?

• 3.1416

• 2.0944

• 1.5708

• 0.84106

What is the sine of pi?

• 0.5

• 1

• 0

• -1

What is the cosine of pi?

• 0.5

• -1

• 0

• 1