Find the direction angle of u=(-7,-10) . Enter your answer as an angle in degrees between and rounded to the nearest hundredth.

Question

Find the direction angle of u=(-7,-10)    . Enter your answer as an angle in degrees between     and     rounded to the nearest hundredth.

Bytelearn · Accepted Answer

Understand Direction Angle: Understand the concept of a direction angle. The direction angle of a vector in the plane is the angle measured counterclockwise from the positive x-axis to the vector. For a vector u = (x, y), the direction angle θ can be found using the arctangent function, where θ = arctan(y/x). However, since the arctangent function only gives values from -π/2 to π/2, we need to adjust the angle depending on the quadrant in which the vector lies.Identify Vector Quadrant: Identify the quadrant in which the vector lies. The vector u = (-7, -10) lies in the third quadrant because both x and y are negative. In the third quadrant, the direction angle is between 180° and 270°.Calculate Arctangent: Calculate the arctangent of the vector's y-coordinate divided by its x-coordinate. θ = arctan(y/x) = arctan(-10/-7) = arctan(10/7). We use a calculator to find the arctangent of 10/7.Adjust for Third Quadrant: Adjust the angle for the third quadrant. Since the arctangent function gives us an angle in the first quadrant, we need to add 180° to get the direction angle in the third quadrant. θ = arctan(10/7) + 180°.Calculate Exact Direction Angle: Calculate the exact value of the direction angle. Using a calculator, we find that arctan(10/7) ≈ 55.00° (rounded to two decimal places). Therefore, θ ≈ 55.00° + 180° = 235.00°.

Find the direction angle of $\mathbf{u}=(-7,-10)$ . Enter your answer as an angle in degrees between $0^\circ$ and $360^\circ$ rounded to the nearest hundredth.

Full solution

More problems from Inverses of trigonometric functions using a calculator

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Find the direction angle of u=(−7,−10)\mathbf{u}=(-7,-10)u=(−7,−10). Enter your answer as an angle in degrees between 0∘0^\circ0∘ and 360∘360^\circ360∘ rounded to the nearest hundredth.

Find the direction angle of $\mathbf{u}=(-7,-10)$ . Enter your answer as an angle in degrees between $0^\circ$ and $360^\circ$ rounded to the nearest hundredth.