Tudor O.

asked • 09/19/22

(Delta) is an angle in standard position whose terminal arm is in quadrant 4 and cos (delta) = 3 / square root (13). Find src (delta)

A) square root (13) / 3

B) - square root (13) / 2

C) 2 / square root (13)

D) - 4 / square root (13)

Inactive Tutor

src? Did you mean sec or sin?
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09/19/22

Inactive Tutor

That is a valid question, Bradford. I was also wondering whether, perhaps, it was not merely a typo, but no other meaning for "src" seemed appropriate here. Based on the available answers--and on the closeness of the spelling--it is likely he / she meant to be asking about sec (delta), which would be: >>> A) square root (13) / 3 because the secant of an angle is equals the reciprocal of cosine of that angle: sec (delta) = 1 / cos (delta) sec (delta) = 1 / (3 / square root (13) sec (delta) = 1 * (square root (13) / 3) >>> sec (delta) = square root (13) / 3 I doubt the questioner was looking for the sine, but that can also quickly be determined: sin (delta))^2 + (cos (delta))^2 = 1 sin (delta))^2 = 1 – (cos (delta))^2 sin (delta)) = +/- square root (1 – (cos (delta))^2) sin (delta)) = +/- square root (1 – (3 / square root (13))^2) sin (delta)) = +/- square root (1 – (9 / 13)) sin (delta)) = +/- square root (1 – (9 / 13)) sin (delta)) = +/- square root (4 / 13) sin (delta)) = +/- 2 / square root (13) ...and, because the sine of an angle is always negative in the 4th quadrant: >>> sin (delta)) = -2 / square root (4 / 13) While we're at it, we could then determine what the tangent of delta is: tan (delta)) = sin (delta) / cos (delta) tan (delta)) = (-2 / square root (13)) / (3 / square root (13)) tan (delta)) = (-2 / square root (13)) * (square root (13) / 3) tan (delta)) = (-2 / 3) * (square root (13) / square root (13) >>> tan (delta) = -2 / 3
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09/20/22

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