Question

Tg(π/3+α) если cosα=0,6 и 3π/2

Answer 1

I hope this helps you

Answer 2

To find the value of tg(π/3 + α), we can use the trigonometric identity:

tan(π/3 + α) = (tan(π/3) + tan(α)) / (1 - tan(π/3) * tan(α))

Since we know that cos(α) = 0.6, we can find sin(α) using the Pythagorean trigonometric identity:

sin^2(α) + cos^2(α) = 1 sin^2(α) + 0.6^2 = 1 sin^2(α) = 1 - 0.6^2 sin^2(α) = 1 - 0.36 sin^2(α) = 0.64 sin(α) = √0.64 sin(α) = 0.8

Now, let's find tan(α):

tan(α) = sin(α) / cos(α) tan(α) = 0.8 / 0.6 tan(α) = 4/3

Now, let's find tan(π/3):

tan(π/3) = √3

Now we can substitute these values into the initial trigonometric identity:

tan(π/3 + α) = (tan(π/3) + tan(α)) / (1 - tan(π/3) * tan(α)) tan(π/3 + α) = (√3 + 4/3) / (1 - √3 * 4/3) tan(π/3 + α) = (√3 + 4/3) / (1 - (4√3)/3) tan(π/3 + α) = (√3 + 4/3) / (1 - (4√3)/3)

To simplify further, we can rationalize the denominator by multiplying both the numerator and the denominator by 3:

tan(π/3 + α) = [(√3 + 4/3) * 3] / [(1 - (4√3)/3) * 3] tan(π/3 + α) = (3√3 + 4) / (3 - 4√3)

So, the value of tan(π/3 + α) is (3√3 + 4) / (3 - 4√3).