Question

If the terminal side of an angle passes through the point P = (-7, 2), what is the value of the angle in radians? Express your answer as a fraction, leaving square roots in the expression where needed.

a) π/4
b) 3π/4
c) -π/4
d) -3π/4

Answer 1

To find the value of the angle in radians, we can use the coordinates of point P = (-7, 2). The angle is measured from the positive x-axis in a counterclockwise direction. Using the Pythagorean theorem and trigonometric functions, we can calculate the angle to be approximately 0.3439 radians.Correct option is b.

Step-by-step explanation:

First, we can find the length of the hypotenuse of the right triangle formed by the coordinates of point P. Using the Pythagorean theorem, we get √((-7)^2 + 2^2) = √53.

Next, we can use the coordinate (-7, 2) to find the sine and cosine of the angle. Since sine = y/hypotenuse and cosine = x/hypotenuse, we have sinθ = 2/√53 and cosθ = -7/√53.

Finally, we can use the inverse sine function to find the angle in radians. sin^-1(2/√53) ≈ 0.3439 radians. Therefore, the value of the angle in radians is approximately 0.3439.