Question

If cos θ≈0.3090, which of the following represents approximate values of sin0 and tan0 , for ?

a. sin θ≈0.9511; tan θ≈ 0.3249
b. sin θ≈0.9511; tan θ ≈3.0780
c. sin θ≈3.2362; tan θ≈ 0.0955
d. sin θ≈3.2362; tan θ≈ 10.4731

Answer 1

Given cos θ ≈ 0.3090, we calculate sin θ by taking the square root of (1 - cos^2 θ) which yields sin θ ≈ 0.9511. To find tan θ, we divide sin θ by cos θ, obtaining tan θ ≈ 3.0780. Therefore, the correct values are sin θ ≈ 0.9511 and tan θ ≈ 3.0780.

Step-by-step explanation:

If cos θ ≈ 0.3090, we need to find the approximate values for sin θ and tan θ. We can use the Pythagorean Theorem which relates the sine, cosine, and tangent for a given angle.

Since we know that for any angle θ in a right-angled triangle:

sin^2 θ + cos^2 θ = 1

We have:

sin^2 θ = 1 - cos^2 θ

sin θ = sqrt(1 - cos^2 θ)

Substituting the given value for cos θ:

sin θ = sqrt(1 - 0.3090^2)

sin θ = sqrt(1 - 0.095481)

sin θ = sqrt(0.904519)

sin θ ≈ 0.9511 (since sin θ is positive in the first and second quadrants and assuming θ is in one of these).

Now, for tan θ, we know that:

tan θ = sin θ / cos θ

So:

tan θ ≈ 0.9511 / 0.3090

tan θ ≈ 3.0780

Therefore, the correct answer is b. sin θ ≈ 0.9511; tan θ ≈ 3.0780.