Trigonometric Equations Quiz

What is the form of the quadratic trinomial used in the first example?

• ax^2 + bx - c

• ax^2 - bx - c

• ax^2 + bx + c

• ax^2 - bx + c

Which angles correspond to the solution of sine of x equals negative one-half?

• pi and 3 pi over 2

• pi over 2 and pi

• pi over 3 and 5 pi over 3

• 7 pi over 6 and 11 pi over 6

What identity is used to substitute sine squared of x in the second example?

• Reciprocal identity

• Quotient identity

• Double angle identity

• Pythagorean identity

Which angles are solutions when cosine of x equals one-half?

• 0 and pi

• pi and 2 pi

• pi over 2 and 3 pi over 2

• pi over 3 and 5 pi over 3

What is the first step in solving the equation with cosine of x plus one equals sine of x?

• Subtract cosine from both sides

• Add one to both sides

• Multiply both sides by two

• Square both sides

Which angle is not a solution to the original equation after verification?

• pi

• 5 pi over 3

• pi over 2

• 3 pi over 2

How are cosecant and cotangent expressed in the final example?

• Using the sum and difference identities

• Using the double angle identity

• Using the reciprocal and quotient identities

• Using the Pythagorean identity

What is the correct solution for the equation involving cosecant and cotangent?

• 5 pi over 3

• 3 pi over 2

• pi over 2

• pi

What is emphasized in the conclusion regarding solutions?

• Verify solutions to avoid extraneous results

• Ignore extraneous solutions

• Always use graphing

• Use only algebraic methods

What is the main focus of the final example?

• Graphing solutions

• Verifying solutions

• Solving quadratic equations

• Using double angle identities