Question

Tg(α+7pi )-cos(2α+ pi/2), sinα=0,6 0< α < pi/2

Answer 1

Tg(α+7pi )-cos(2α+ pi/2), sinα=0,6 0< α < pi/2 

Answer 2

To evaluate the expression Tg(α + 7π) - cos(2α + π/2) when sin(α) = 0.6 and 0 < α < π/2, we first need to find the values of tangent and cosine for the given angles.

Given: sin(α) = 0.6 0 < α < π/2

We can find cos(α) using the Pythagorean identity for sine and cosine:

sin^2(α) + cos^2(α) = 1

Since sin(α) = 0.6, we can calculate:

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

Now that we have the values of sin(α) and cos(α), we can find tan(α):

tan(α) = sin(α) / cos(α) tan(α) = 0.6 / 0.8 tan(α) = 0.75

Now we can proceed to evaluate the given expression:

Tg(α + 7π) - cos(2α + π/2)

Since 7π is a multiple of 2π, adding or subtracting it from an angle doesn't change its trigonometric function values. Therefore:

tan(α + 7π) = tan(α) = 0.75

Next, we need to find cos(2α + π/2):

cos(2α + π/2) = cos(2α) * cos(π/2) - sin(2α) * sin(π/2)

Since cos(π/2) = 0 and sin(π/2) = 1, the expression simplifies to:

cos(2α + π/2) = -sin(2α)

Using the double-angle identity for sine:

sin(2α) = 2 * sin(α) * cos(α)

We already know sin(α) = 0.6 and cos(α) = 0.8, so:

sin(2α) = 2 * 0.6 * 0.8 sin(2α) = 0.96

Now, we can substitute the values into the original expression:

Tg(α + 7π) - cos(2α + π/2) = 0.75 - (-sin(2α)) = 0.75 - (-0.96)

Now, let's calculate:

Tg(α + 7π) - cos(2α + π/2) = 0.75 + 0.96 = 1.71

So, the final value of the expression is 1.71 when sin(α) = 0.6 and 0 < α < π/2.