Question

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Given that ( cos theta=frac{sqrt{50}}{10} ) and ( cot theta ) is negative determine ( theta ) and cote. Enter the angle ( theta ) in degrees from the interval ( left(0{ᶜᶦʳᶜ}, 360{ᶜᶦʳᶜ}

Answer 1

To determine the value of theta and cot(theta), we can use the given value of cos(theta) and the fact that cosine is positive in the 4th quadrant when cot(theta) is negative. We can solve for theta by using the inverse tangent function and find cot(theta) using the relationship cot(theta) = 1/tan(theta).

Step-by-step explanation:

To determine the value of theta, we can use the given value of cos(theta) and the fact that cosine is positive in the 4th quadrant when cot(theta) is negative. Since cos(theta) = sqrt(50)/10, we can say that cos(theta) = x/r, where x = sqrt(50) and r = 10. Using the Pythagorean Identity x^2 + y^2 = r^2, we can solve for y. After finding the values of x and y, we can use the inverse tangent function to determine the value of theta.

To find cot(theta), we can use the relationship cot(theta) = 1/tan(theta). Since we have already found the value of theta, we can substitute this value into the tangent function to find the value of cot(theta).