Write the first trigonometric function in terms of the second for 𝜃 in the given quadrant. tan(𝜃), cos(𝜃); 𝜃 in Quadrant II

Answer 1

Write the first trigonometric function in terms of the second for 𝜃 in the given quadrant. tan(𝜃), cos(𝜃); 𝜃 in Quadrant II

Assuming tan(θ) is the first function and cos(θ) is the second, we need a couple of identities:

1. tan (θ) = sin (θ)/cos (θ)
2. sin (θ) = ±√(1-cos²(θ))

Since θ is in QII, we can be sure that sin (θ) = √(1-cos²(θ)), or in other words, just the positive root. This is because sin (θ) is positive everywhere in QII.

Then we have:

tan (θ) = sin (θ)/cos (θ)

tan (θ) = √(1-cos²(θ))/cos (θ)

Answer 2

tan θ = sin θ / cos θ, by definition.

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