If sec 2A = 1 / sin 13A, determine the value of A in degrees. If sec 2A = 1 / sin 13A, determine the value of A in degrees. A. 7 C. 3 B. 6 D. 5 Solution Click here to… Jhun Vert Thu, 07/04/2024 - 18:56 Solution Click here to expand or collapse this section $\sec 2A = \dfrac{1}{\sin 13A}$ $\sec 2A = \csc 13A$ $\sec 2A = \sec (90^\circ - 13A)$ Hence, $2A = 90^\circ - 13A$ $15A = 90^\circ$ $A = 6^\circ$ You can also do trial and error using the choices $\sec 2A = \dfrac{1}{\sin 13A}$ $\dfrac{1}{\cos 2A} = \dfrac{1}{\sin 13A}$ Try A = 3°: $\dfrac{1}{\cos 6^\circ} \ne \dfrac{1}{\sin 39^\circ}$ ← not ok Try A = 5°: $\dfrac{1}{\cos 10^\circ} \ne \dfrac{1}{\sin 65^\circ}$ ← not ok Try A = 6°: $\dfrac{1}{\cos 12^\circ} = \dfrac{1}{\sin 78^\circ}$ ← ok! Try A = 7°: $\dfrac{1}{\cos 14^\circ} \ne \dfrac{1}{\sin 91^\circ}$ ← not ok Answer: A = 6° Log in to post comments Log in to post comments

Solution Click here to… Jhun Vert Thu, 07/04/2024 - 18:56 Solution Click here to expand or collapse this section $\sec 2A = \dfrac{1}{\sin 13A}$ $\sec 2A = \csc 13A$ $\sec 2A = \sec (90^\circ - 13A)$ Hence, $2A = 90^\circ - 13A$ $15A = 90^\circ$ $A = 6^\circ$ You can also do trial and error using the choices $\sec 2A = \dfrac{1}{\sin 13A}$ $\dfrac{1}{\cos 2A} = \dfrac{1}{\sin 13A}$ Try A = 3°: $\dfrac{1}{\cos 6^\circ} \ne \dfrac{1}{\sin 39^\circ}$ ← not ok Try A = 5°: $\dfrac{1}{\cos 10^\circ} \ne \dfrac{1}{\sin 65^\circ}$ ← not ok Try A = 6°: $\dfrac{1}{\cos 12^\circ} = \dfrac{1}{\sin 78^\circ}$ ← ok! Try A = 7°: $\dfrac{1}{\cos 14^\circ} \ne \dfrac{1}{\sin 91^\circ}$ ← not ok Answer: A = 6° Log in to post comments

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