Trigonometric Equations Quiz

The video tutorial covers solving trigonometric equations using various methods such as factoring, the difference of squares, and the double angle formula. It explains how to handle equations involving sine and cosine, and the use of the Pythagorean identity to simplify mixed trig functions. The tutorial also discusses the limitations of inverse trigonometric functions, emphasizing the difference between solving with sine and arc sine.

What is the first step in solving the equation sine squared plus 2 sine x minus 3 equals 0?

• Factor by substitution

• Use the quadratic formula

• Use the Pythagorean identity

• Graph the equation

When factoring a trinomial with a leading coefficient, what method is used to simplify the process?

• Graphing the equation

• Completing the square

• Using the quadratic formula

• Factoring by grouping

In the equation 4 sine squared minus 1 equals 0, what technique is used to factor it?

• Quadratic formula

• Difference of squares

• Substitution

• Completing the square

What is the double angle formula for sine 2x?

• 2 cosine squared x minus 1

• sine squared x minus cosine squared x

• 1 minus 2 sine squared x

• 2 sine x cosine x

Why should you avoid dividing by cosine when solving the equation sine 2x equals cosine x?

• It makes the equation more complex

• It changes the range of the function

• It results in a division by zero

• It causes a loss of solutions

What is the range of the arc sine function?

• -pi to pi

• 0 to 2pi

• -pi/2 to pi/2

• 0 to pi

How many solutions can you expect when solving a trigonometric equation using the sine function?

• One solution

• No solutions

• Two solutions

• An unlimited number of solutions

What is the correct way to express the general solution for sine x equals square root of 3 over 2?

• x = pi/3 + pi n

• x = 2pi/3

• x = pi/3

• x = pi/3 + 2pi n

Which quadrant does the arc sine function not exist in?

• Quadrant 4

• Quadrant 1

• Quadrant 2

• Quadrant 3

What is the main difference between solving trigonometric equations and using inverse trigonometric functions?

• The number of solutions

• The type of trigonometric function used

• The method of solving

• The complexity of the equation