#1**+5 **

We're looking for the secant of an angle whose sin = 4/7

Sec = r /x and x = sqrt (7^2 - 4^2) = sqrt (49 - 16) = sqrt (33)

So.....sec (theta) = 7 / sqrt(33) = (7/33)*sqrt(33)

[Since the sine inverse only has a range of -pi/2 to pi/2, theta must fall in either the 1st or 4th quadrant......so......the secant is positive in both of these ]

CPhill
Mar 9, 2017

#1**+5 **

Best Answer

We're looking for the secant of an angle whose sin = 4/7

Sec = r /x and x = sqrt (7^2 - 4^2) = sqrt (49 - 16) = sqrt (33)

So.....sec (theta) = 7 / sqrt(33) = (7/33)*sqrt(33)

[Since the sine inverse only has a range of -pi/2 to pi/2, theta must fall in either the 1st or 4th quadrant......so......the secant is positive in both of these ]

CPhill
Mar 9, 2017