Trigonometry Trigonometric Equations 3

Question 1

Solve sin(x) + cos(x) = 1 for x in [0, 2π).

Accepted Answer

x = 0, π/2

Answer

x = 0, π

Answer

x = π/4, 5π/4

Answer

x = π/2, 3π/2

Question 2

Which method most directly solves sin(x) = cos(x)?

Accepted Answer

Divide both sides by cos(x) to obtain tan(x) = 1

Answer

Square both sides

Answer

Apply a Pythagorean identity

Answer

Use the double-angle formula

Question 3

Solve cos(x) = sin(x) for x in [0, 2π).

Accepted Answer

x = π/4, 5π/4

Answer

x = π/3, 4π/3

Answer

x = π/6, 7π/6

Answer

x = π/2, 3π/2

Question 4

What is the period of solutions for the equation 2sin(3x) − 1 = 0?

Accepted Answer

2π/3

Answer

π

Answer

3π

Answer

π/3

Question 5

Solve sin(x/2) = √2/2 for x in [0, 4π).

Accepted Answer

x = π/2, 3π/2

Answer

x = π/4, 3π/4

Answer

x = π, 3π

Answer

x = π/4, 7π/4

Question 6

Solve sin(2x) = −√3/2 for x in [0, 2π).

Accepted Answer

x = 2π/3, 5π/6, 5π/3, 11π/6

Answer

x = π/3, π/2, 4π/3, 3π/2

Answer

x = π/6, π/3, 7π/6, 4π/3

Answer

x = π/4, 3π/4, 5π/4, 7π/4

Question 7

For the equation 3sin(x) + 2 = 0, which expression gives the reference angle?

Accepted Answer

arcsin(2/3)

Answer

arccos(2/3)

Answer

arctan(2/3)

Answer

π − arcsin(2/3)