Question

Solve the equation sin⁡(3x−π/4)=−1 for x in the range −2020≤x≤2020. How many roots does the equation have?

a) 0
b) 1
c) 2
d) 3

Answer 1

To solve the equation sin(3x−π/4)=−1 for x in the range -2020≤x≤2020, rewrite the equation as 3x-π/4 = arcsin(-1), solve for x, and find that the equation has b) 1 root.

Step-by-step explanation:

To solve the equation sin⁡(3x−π/4)=−1 for x in the range -2020≤x≤2020, we need to find the values of x that satisfy the equation.

To solve the equation, we need to rewrite it as 3x-π/4 = arcsin(-1). The arcsin(-1) is equivalent to -π/2. So, we have 3x-π/4 = -π/2. Solving for x, we get x = -π/12.

Therefore, the equation has 1 root in the given range.