vec(u)=(8,6) Find the direction angle of vec(u). Enter your answer as an angle in degrees between 0^(@) and 360^(@) rounded to the nearest hundredth. theta=◻" 。 "

Question

vec(u)=(8,6) Find the direction angle of  vec(u). Enter your answer as an angle in degrees between  0^(@) and  360^(@) rounded to the nearest hundredth.  theta=◻" 。 "

Bytelearn · Accepted Answer

Calculate Tangent Ratio: To find the direction angle of the vector $ \vec{u} = (8,6) $, we need to calculate the angle $ \theta $ that the vector makes with the positive x-axis. The direction angle can be found using the arctangent function, which is the inverse of the tangent function. The tangent of the angle is the ratio of the y-coordinate to the x-coordinate of the vector. So, we calculate $ \tan(\theta) = \frac{y}{x} $.Substitute Values: Substitute the values of the vector $ \vec{u} = (8,6) $ into the formula to get $ \tan(\theta) = \frac{6}{8} = \frac{3}{4} $.Use Arctangent Function: Now, we use the arctangent function to find the angle $ \theta $. We calculate $ \theta = \arctan\left(\frac{3}{4}\right) $. This will give us the angle in radians, which we then convert to degrees.Convert to Degrees: Using a calculator, we find that $ \theta \approx \arctan\left(\frac{3}{4}\right) $ in degrees is approximately 36.87 degrees.Check Quadrant: Since the vector $ \vec{u} = (8,6) $ is in the first quadrant (both x and y are positive), the direction angle $ \theta $ is already between 0 and 90 degrees. Therefore, we do not need to adjust the angle further.

$\vec{u}=(8,6)$ $\newline$ Find the direction angle of $\vec{u}$ . Enter your answer as an angle in degrees between $0^{\circ}$ and $360^{\circ}$ rounded to the nearest hundredth. $\newline$ $\theta= \square^{\circ}$

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More problems from Inverses of sin, cos, and tan: degrees

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u⃗=(8,6) \vec{u}=(8,6) u=(8,6)\newlineFind the direction angle of u⃗ \vec{u} u. Enter your answer as an angle in degrees between 0∘ 0^{\circ} 0∘ and 360∘ 360^{\circ} 360∘ rounded to the nearest hundredth.\newlineθ=□∘ \theta= \square^{\circ} θ=□∘

$\vec{u}=(8,6)$ $\newline$ Find the direction angle of $\vec{u}$ . Enter your answer as an angle in degrees between $0^{\circ}$ and $360^{\circ}$ rounded to the nearest hundredth. $\newline$ $\theta= \square^{\circ}$