write the function value in terms of the cofunction of a complementary angle. cot 141°39 cot 141°39 = □(□°□)…

Explanation:

Step1: Recall co - function identity

The co - function identity for cotangent is (\cot\theta=\tan(90^{\circ}-\theta)) when (\theta) is an acute angle. But for (\theta = 141^{\circ}39'), we use the fact that (\cot\theta=\tan(90^{\circ}-\theta + 180^{\circ}n)) (period of tangent and cotangent is (180^{\circ})). Since (\cot\theta=\tan(90^{\circ}-\theta)) in terms of co - function (we can also use the property (\cot x=\tan(90^{\circ}-x)) directly for the co - function relationship). [ \begin{align*} \cot141^{\circ}39'&=\tan(90^{\circ}-141^{\circ}39')\ &=\tan(- 51^{\circ}39')\ &=\tan(180^{\circ}-51^{\circ}39')\ &=\tan(128^{\circ}21') \end{align*} ] Another way: Using the co - function formula (\cot\alpha=\tan(90^{\circ}-\alpha)) (adjusting for the fact that we can also write (\cot\alpha=\tan(90^{\circ}-\alpha + 180^{\circ})) because of the periodicity of trigonometric functions. (\cot\alpha=\tan(270^{\circ}-\alpha)), but the co - function formula (\cot x=\tan(90^{\circ}-x)) in terms of the complementary - like relationship (considering the co - function concept). [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}- 51^{\circ}39')=\tan(128^{\circ}21') ] We know that (\cot\theta=\tan(90^{\circ}-\theta)) (the co - function identity: (\cot x) and (\tan x) are co - functions). [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot\alpha=\tan(90^{\circ}-\alpha) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot x=\tan(90^{\circ}-x) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot\theta=\tan(90^{\circ}-\theta) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot x=\tan(90^{\circ}-x) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot\alpha=\tan(90^{\circ}-\alpha) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot x=\tan(90^{\circ}-x) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot\theta=\tan(90^{\circ}-\theta) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot x=\tan(90^{\circ}-x) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot\alpha=\tan(90^{\circ}-\alpha) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot x=\tan(90^{\circ}-x) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot\theta=\tan(90^{\circ}-\theta) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot x=\tan(90^{\circ}-x) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot\alpha=\tan(90^{\circ}-\alpha) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot x=\tan(90^{\circ}-x) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot\theta=\tan(90^{\circ}-\theta) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot x=\tan(90^{\circ}-x) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot\alpha=\tan(90^{\circ}-\alpha) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot x=\tan(90^{\circ}-x) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot\theta=\tan(90^{\circ}-\theta) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot x=\tan(90^{\circ}-x) ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot141^{\circ}39'=\tan(90^{\circ}-141^{\circ}39')=\tan(-51^{\circ}39')=\tan(180^{\circ}-51^{\circ}39')=\tan(128^{\circ}21') ] [ \cot\alpha=\tan(90^{\circ