Suppose a is in standard position ,whose terminal side is parallel with the line y-5x and a is in 2 quadrant ,find sin a
To find the value of sin(a), we need to determine the y-coordinate of the point where the terminal side of angle a intersects the unit circle.
Given that the terminal side of angle a is parallel to the line y-5x and is in the second quadrant, we can determine the slope of the line and find its corresponding angle in the unit circle.
The slope of the line y-5x can be found by rearranging the equation into slope-intercept form (y = mx + b):
y - 5x = 0
y = 5x
This gives us the slope, which is 5. The angle of this line can be found using the inverse tangent function (arctan). So, we have:
angle = arctan(5)
Now that we have the angle in radians, we can determine the y-coordinate on the unit circle by using the sine function. The unit circle has a radius of 1, and the y-coordinate represents the sine value.
sin(a) = sin(angle)
Using a calculator or trigonometric table, evaluate sin(angle) to find the value of sin(a).