Given the following point on the unit circle, find the angle, to the nearest tenth of a degree (if necessary), of the terminal side through that point, 0^(@)

Question

Given the following point on the unit circle, find the angle, to the nearest tenth of a degree (if necessary), of the terminal side through that point,  0^(@) <= theta < 360^(@).  P=((sqrt6)/(4),-(sqrt10)/(4)) Answer:

Bytelearn · Accepted Answer

Calculate Tangent Ratio: To find the angle of the terminal side through the point P on the unit circle, we need to use the inverse trigonometric functions. Since we have both the x-coordinate (cosine value) and the y-coordinate (sine value), we can use the arctangent function, which gives us the angle whose tangent is the ratio of the y-coordinate to the x-coordinate.Use Arctangent Function: First, we calculate the tangent of the angle, which is the ratio of the y-coordinate to the x-coordinate of the point P. tan(theta) = y/x = (-(sqrt10)/(4)) / ((sqrt6)/(4)) tan(theta) = -(sqrt10)/(sqrt6) tan(theta) = -sqrt(10/6) tan(theta) = -sqrt(5/3)Consider Quadrant: Next, we use the arctangent function to find the angle whose tangent is -sqrt(5/3). However, since the arctangent function only gives us the principal value (between -90 degrees and 90 degrees), we need to consider the quadrant in which the point P lies to find the correct angle in the range [0, 360) degrees.Find Angle in Radians: The point P has a positive x-coordinate and a negative y-coordinate, which places it in the fourth quadrant. The arctangent of a negative number is also negative, which corresponds to an angle in the fourth quadrant. Therefore, we can use the arctangent function directly to find the angle in the fourth quadrant. theta = arctan(-sqrt(5/3))Convert to Degrees: Using a calculator to find the arctan(-sqrt(5/3)), we get an angle in radians. To convert it to degrees, we multiply by 180/pi. theta = arctan(-sqrt(5/3)) * (180/pi)Find Coterminal Angle: After performing the calculation, we find that the angle is approximately -58.3 degrees. However, since we want the angle in the range [0, 360) degrees, we add 360 degrees to the negative angle to find the positive coterminal angle. theta = -58.3 + 360 theta = 301.7 degrees

Given the following point on the unit circle, find the angle, to the nearest tenth of a degree (if necessary), of the terminal side through that point, 0^{\circ} \leq \theta<360^{\circ} . $\newline$ $P=\left(\frac{\sqrt{6}}{4},-\frac{\sqrt{10}}{4}\right)$ $\newline$ Answer:

Full solution

More problems from Evaluate variable expressions for number sequences

Related topics