given sin28.4=.4756, cos28.4=.8796, and tan28.4=.5407 find the cot of 61.6

Answer:The cotangent of 61.6° is .5407.Step-by-step explanation:Refer to the sketch attached.61.6° + 28.4° = 90°. In other words, 61.6° is the complementary angle of 28.4°.Consider a right triangle OAB with a 61.6° angle [tex]\rm O\hat{A}B[/tex]. The other acute angle [tex]\rm O\hat{B}A[/tex] will be 28.4°.[tex]\displaystyle \tan{61.6\textdegree{}}=\tan{\rm O\hat{A}B} = \frac{\text{Opposite of }\rm O\hat{A}B}{\text{Adjacent of }\rm O\hat{A}B} = \frac{a}{b}[/tex].The cotangent of an angle is the reciprocal of its tangent.[tex]\displaystyle \cot{61.6^{\circ}}=\frac{1}{\tan{\rm O\hat{B}A}} = \frac{\text{Adjacent of }\rm O\hat{B}A}{\text{Opposite of }\rm O\hat{B}A} = \frac{a}{b} = \tan{\rm O\hat{A}B} = \tan{28.4^{\circ}}[/tex]. In other words,[tex]\cot{61.6^{\circ}} = \tan{28.4^{\circ}} \approx 0.5407[/tex].