Janice is roller skating at a constant speed away from her house. The first half of the street is flat, but the second half has
a steep upward hill. Janice moves more slowly as she skates up the hill.
Which graph shows Janice's position as she roller skates away from her house?
A. Z
B. X
C. W
D. Y
Which graph shows Janice's position as she roller skates away from her house?
A. Z
B. X
C. W
D. Y
2 answers:
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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}
__
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.
