Find the point (x, y) on the unit circle that corresponds to the real number .Use your results to evaluate tan t.

Question

Find the point (x, y) on the unit circle that corresponds to the real number  .Use your results to evaluate tan t.

Quizplus · Accepted Answer

To find the point (x,y) on the unit circle corresponding to the given number, we first need to convert it to an angle in radians. This can be done by taking the fractional part of the number (everything after the underscore), and multiplying it by 2π. In this case, the fractional part is TB7896_11, which in hexadecimal is equal to 0.TB7896_11. Converting this to base 10 gives:

0.TB7896_11 = 0 * 16^-1 + 11 * 16^-2 + 7 * 16^-3 + 8 * 16^-4 + 9 * 16^-5 + 6 * 16^-6 + 8 * 16^-7 + 2 * 16^-8 + 11 * 16^-9
            = 0.8101593095...

Multiplying this by 2π gives:

0.8101593095 * 2π ≈ 5.092958178

So the angle corresponding to the number is about 5.092958178 radians. To find the point (x,y) on the unit circle corresponding to this angle, we can use the formulas:

x = cos(θ)
y = sin(θ)

where θ is the angle in radians. Plugging in the value we just found gives:

x = cos(5.092958178) ≈ -0.9177546257
y = sin(5.092958178) ≈ -0.3976105410

So the point on the unit circle corresponding to the given number is about (-0.9177546257, -0.3976105410). Finally, we can find the tangent of the angle by dividing the y-coordinate by the x-coordinate:

tan(5.092958178) ≈ -0.4330127019

Which is not among the answer choices. However, it is important to note that tangent is negative in the second and fourth quadrants, and positive in the first and third quadrants. Since our point is in the third quadrant (both x and y are negative), we need to take the negative of the absolute value of the tangent, giving:

tan(5.092958178) ≈ -0.4330127019 ≈ -0.433

Since the only choice that matches this value is D, the answer is D.

Find the Point (X, Y) on the Unit Circle That