Trigonometric Equations and General Solutions Quiz

What is the first step in solving the equation 2cos(X) - 1 = 0?

• Divide both sides by 2

• Multiply both sides by 2

• Add 1 to both sides

• Subtract 1 from both sides

Where on the unit circle is cosine equal to 1/2?

• At π/2 and 3π/2

• At π/3 and 5π/3

• At 0 and π

• At π/4 and 7π/4

What is the general solution for the equation 2cos(X) - 1 = 0?

• X = π/6 + πn and X = 5π/6 + πn

• X = π/4 + πn and X = 3π/4 + πn

• X = π/3 + 2πn and X = 5π/3 + 2πn

• X = π/2 + 2πn and X = 3π/2 + 2πn

What is the first step in solving the equation 4cos²(X) - 3 = 0?

• Subtract 3 from both sides

• Add 3 to both sides

• Multiply both sides by 4

• Divide both sides by 4

What angles correspond to cosine being ±√3/2 on the unit circle?

• π/4 and 3π/4

• π/6 and 5π/6

• π/3 and 2π/3

• π/2 and 3π/2

What is the general solution for the equation 4cos²(X) - 3 = 0?

• X = π/4 + 2πn and X = 3π/4 + 2πn

• X = π/2 + πn and X = 3π/2 + πn

• X = π/6 + πn and X = 5π/6 + πn

• X = π/3 + πn and X = 2π/3 + πn

How is secant related to cosine?

• Secant is the derivative of cosine

• Secant is the inverse of cosine

• Secant is the reciprocal of cosine

• Secant is the square of cosine

What is the first step in solving the equation cos(X) - sec(X) = 0?

• Add sec(X) to both sides

• Subtract cos(X) from both sides

• Convert sec(X) to 1/cos(X)

• Multiply both sides by cos(X)

Where on the unit circle is cosine equal to ±1?

• At π/3 and 5π/3

• At π/4 and 7π/4

• At π/2 and 3π/2

• At 0 and π

What is the general solution for the equation cos(X) - sec(X) = 0?

• X = 2π/3 + πn

• X = π/4 + πn

• X = π/2 + 2πn

• X = πn