Angle A is in standard position and terminates in quadrant IV. If sec(A) = 4/3 , complete the steps to find cot(A). Use the identity _____ to find the value of ___(A).
Accepted Solution
A:
If sec(A) = 4/3, then the value cot(A) is [tex]cot(A)=\frac{3\sqrt{7}}{7}[/tex]The given trigonometric identity is:[tex]sec(A)=\frac{4}{3}[/tex].........................(*)Note that:[tex]sec(A)=\frac{Hypotenuse}{Adjacent}[/tex].........................(**)Comparing (*) and (**)Hypotenuse = 4Adjacent = 3Find the opposite using the Pythagoras theoremHypotenuse² = Opposite² + Adjacent²4² = Opposite² + 3²Opposite² = 4² - 3²Opposite² = 16 - 9Opposite² = 7Opposite = √7cot(A) = Adjacent/Oppositecot(A) = 3/√7Rationalize the expression[tex]cot(A)=\frac{3\sqrt{7}}{7}[/tex]Learn more here: