Trigonometric Equations and Functions

The video tutorial explains how to solve the trigonometric equation cosine squared X minus cosine X minus 2 equals 0. It begins by solving the equation on the interval from 0 to 360 degrees and then generalizes to all solutions. The equation is transformed into a quadratic form, solved by factoring, and analyzed for valid cosine values. The tutorial uses the unit circle and cosine graph to illustrate why cosine X cannot equal 2 and identifies the valid solution where cosine X equals -1. Finally, it expresses all solutions in both degrees and radians, emphasizing coterminal angles.

What is the first step in solving the trigonometric equation cosine squared x - cosine x - 2 = 0?

• Convert the equation to a quadratic form

• Find the derivative of the equation

• Use the Pythagorean identity

• Graph the equation

How can the equation y^2 - y - 2 = 0 be solved?

• By using the quadratic formula

• By graphing the equation

• By completing the square

• By factoring into two binomials

What are the factors of -2 that add up to -1 in the equation y^2 - y - 2 = 0?

• 1 and 2

• -2 and 1

• -1 and -2

• -1 and 2

Why is cosine x = 2 not a valid solution?

• Because cosine x can only be positive

• Because the maximum value of cosine x is 1

• Because cosine x can only be zero

• Because cosine x can only be negative

What is the maximum value of the cosine function?

• 2

• 1

• 0

• -1

At what angle does the cosine function have a value of -1?

• 270 degrees

• 0 degrees

• 90 degrees

• 180 degrees

What is the period of the cosine function?

• 270 degrees

• 90 degrees

• 360 degrees

• 180 degrees

How can all solutions for the angle be expressed in degrees?

• 180 degrees + 180 degrees x K

• 90 degrees + 360 degrees x K

• 180 degrees + 360 degrees x K

• 270 degrees + 360 degrees x K

How can all solutions for the angle be expressed in radians?

• PI + PI x K

• PI + 2PI x K

• 2PI + PI x K

• 2PI + 2PI x K

What is the suggested interval to initially solve a trigonometric equation?

• 0 to 90 degrees

• 0 to 360 degrees

• 0 to 180 degrees

• 0 to 270 degrees