Question

I’m not sure the answer. help!!

Answer 1

Answer:

  x = {-5π/4, -3π/4, 3π/4, 5π/4}

Step-by-step explanation:

You know that sec(x) = 1/cos(x), so this is equivalent to ...

  cos(x) = -1/√2

The cosine has a magnitude of 1/√2 for an angle of 45°, or π/4 radians. It is negative in the 2nd and 3rd quadrants. Angles in those quadrants that have a reference angle of π/4 are ...

  3π/4, 5π/4

We also want angles in the range -2π to 0, so all of the solutions will be ...

  sec(x) = -√2 for x = {-5π/4, -3π/4, 3π/4, 5π/4}

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We like to use the x-intercept as the solution when graphing, so we write the given equation as ...

  sec(x) +√2 = 0

The graph verifies the above solutions.