Question

Express tan θ in terms of sec θ for θ in Quadrant II. tan θ = _____

Answer 1

To express tan θ in terms of sec θ for θ in Quadrant II, use the trigonometric identity tan θ = sec θ * sin θ.

Step-by-step explanation:

To express tan θ in terms of sec θ for θ in Quadrant II, we can use trigonometric identities. In the second quadrant, the sine and cosine values are both positive. We know that the tangent is equal to the sine divided by the cosine, so we can write:

tan θ = sin θ / cos θ

Since both sin θ and cos θ are positive in Quadrant II, we can rewrite cos θ as 1 / sec θ:

tan θ = sin θ / (1 / sec θ) = sec θ * sin θ