Solving Trigonometric Equations with Multiple Angles

What is the value of x when sine(2x) = 1/2 within the interval [0, 2π]?

• All of the above

• 5π/12

• π/12

• 13π/12

How many solutions are there for sine(2x) = 1/2 in the interval [0, 2π]?

• 3

• 5

• 2

• 4

Which of the following is a solution for tangent(3x) = -1 in the interval [0, 2π]?

• 11π/12

• 15π/12

• π/4

• 7π/12

What is the general form of the solution for tangent(3x) = -1?

• π/4 + π/3n

• 3π/4 + π/3n

• 3π/4 + πn

• π/4 + πn

How many solutions are there for tangent(3x) = -1 in the interval [0, 2π]?

• 6

• 4

• 2

• 8

If tangent(x) has 2 solutions in [0, 2π], how many solutions does tangent(3x) have?

• 2

• 8

• 4

• 6

What is the only solution for cosine(x/2) = -1/2 in the interval [0, 2π]?

• 2π/3

• 4π/3

• 4π/3

• 8π/3

Why does cosine(x/2) = -1/2 have only one solution in [0, 2π]?

• Because x/2 reduces the number of solutions

• Because the period of cosine is 2π

• Because cosine is positive in all quadrants

• Because cosine is negative in only one quadrant

How many solutions does cosine(2x) = -1/2 have in the interval [0, 2π]?

• 4

• 2

• 1

• 3

If cosine(x) has 2 solutions in [0, 2π], how many solutions does cosine(4x) have?

• 8

• 6

• 4

• 2