Find the exact value of cos(theta) for an angle (theta) with tan (theta)= -2/3 and with its terminal side in Quadrant II.

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Step-by-step explanation:

Since we are in quadrant two, cosine value is negative while sine value is positive.

We are going to use the Pythagorean Identity: .

Since cosine and secant are reciprocals then they will have the same sign as along as they both exist.

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I don't see this answer as I'm going to rationalize the denominator.

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b

Step-by-step explanation:

1 + tan²theta = sec²theta

1 + (-2/3)² = sec²theta

1 + 4/9 = sec²theta

13/9 = sec²theta

sec theta = -sqrt(13)/3

Because Quadrant 2

cos theta = 1 ÷ sec theta

Cos there = -3/sqrt(13)

-3sqrt(13)/13

After rationalization