Trigonometry Trigonometric Equations 2

Question 1

Solve sin²(x) = 1 for x in [0, 2π).

Accepted Answer

x = π/2, 3π/2

Answer

x = 0, π

Answer

x = π/4, 3π/4, 5π/4, 7π/4

Answer

x = π/2 only

Question 2

Solve 2cos²(x) − cos(x) − 1 = 0 for x in [0, 2π).

Accepted Answer

x = 0, 2π/3, 4π/3

Answer

x = π/3, π, 5π/3

Answer

x = π/2, π, 3π/2

Answer

x = π/6, π/2, 7π/6

Question 3

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

Accepted Answer

x = π/4, 5π/4

Answer

x = π/4, 3π/4

Answer

x = π/6, 5π/6

Answer

x = π/3, 4π/3

Question 4

What substitution simplifies solving 2sin²(x) + 3sin(x) − 2 = 0?

Accepted Answer

Let u = sin(x)

Answer

Let u = cos(x)

Answer

Let u = tan(x)

Answer

Let u = sin(2x)

Question 5

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

Accepted Answer

x = 0, 2π/3, 4π/3

Answer

x = π/3, π, 5π/3

Answer

x = π/4, π/2, 7π/4

Answer

x = 0, π/3, 5π/3

Question 6

How many solutions does sin(x) = 0.8 have in the interval [0, 2π)?

Accepted Answer

2

Answer

0

Answer

1

Answer

4

Question 7

Solve tan²(x) − 3 = 0 for x in [0, 2π).

Accepted Answer

x = π/3, 2π/3, 4π/3, 5π/3

Answer

x = π/6, 5π/6, 7π/6, 11π/6

Answer

x = π/4, 3π/4, 5π/4, 7π/4

Answer

x = π/3, π, 5π/3