Trigonometry 7th Edition

Required six T-functions are- $\sin A = \frac{3}{4}$ , $\\csc A = \frac{4}{3}$ $\\cos A = \frac{\sqrt 7}{4}$ , $\\sec A = \frac{4}{\sqrt 7}$ $\\tan A = \frac{3}{\sqrt 7}$ , $\\\cot A = \frac{\sqrt 7}{3}$
Steps to Answer- First we will draw the diagram of triangle ABC and then use the given information and Pythagoras Theorem to solve for 'c'- $c^{2} =a^{2} + b^{2}$ $c^{2} = 3^{2} + (\sqrt 7)^{2}$ $c^{2} = 9 + 7$ $c^{2} = 16$ therefore $c = \sqrt 16$ = 4 Now we can write the required six T-functions of A using a = 3, $b= \sqrt 7$ and c = 4 $\sin A = \frac{a}{c} = \frac{3}{4}$ $\\csc A = \frac{c}{a} = \frac{4}{3}$ $\\cos A = \frac{b}{c} = \frac{\sqrt 7}{4}$ $\\sec A = \frac{c}{b} = \frac{4}{\sqrt 7}$ $\\tan A = \frac{a}{b} = \frac{3}{\sqrt 7}$ $\\\cot A = \frac{b}{a} = \frac{\sqrt 7}{3}$