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forsale [732]
3 years ago
8

Given that tan0= -1, what is the value of sec0, for 3pi/2<0<2pi?

Mathematics
2 answers:
Maru [420]3 years ago
7 0

Answer: Choice B. sqrt(2)

Draw out a right triangle in quadrant IV as you see in the attached image below. The horizontal and vertical legs are both 1 unit long. To ensure that the signs are properly set up, I am making the vertical leg BC have a label "-1" to mean this is below the x axis. Note how

tan(theta) = opposite/adjacent = BC/AB = -1/1 = -1

Use the pythagorean theorem to find that the hypotenuse AC is sqrt(2) units long

a^2 + b^2 = c^2

(1)^2 + (1)^2 = c^2

2 = c^2

c^2 = 2

c = sqrt(2)

The secant of theta is the ratio of the hypotenuse over the adjacent side, so we end up with

sec(theta) = hypotenuse/adjacent

sec(theta) = AC/AB

sec(theta) = sqrt(2)/1

sec(theta) = sqrt(2) which is why choice B is the answer

Eddi Din [679]3 years ago
7 0

Answer:

B. on E2020

Step-by-step explanation:

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