Sean \( x, y, z \) las medidas de los ángulos interiores de un triángulo tales que: \( \cot (x)+\cot (\mathrm{y})=-3 \tan (\mathrm{z}) \cot (\mathrm{x}) \cot (\mathrm{y}) \). Determine tan \( (\mathrm{x}) \) en función del ángulo " y ".

(d) Quando fazemos determinaçōes experimentais de uma grandeza \( X \), representamos seu valor numérico final acompanhado do erro \( \Delta X \) associado à medida, na forma \( X \pm \Delta X \). Para calcularmos o valor de uma funçāo \( f(X \pm \Delta X) \), utilizamos a regra \[ f(X \pm \Delta X)=f(X) \pm f^{\prime}(X) \Delta X \] Obtenha as fórmulas referentes a (i) \( \sin (X \pm \Delta X) \) e (ii) \( \cos (X \pm \Delta X) \)

A pylon \( \$ \$ 23.7 \$ \$ \mathrm{~m} \) high casts a shadow \( \$ \$ 46.8 \$ \$ \mathrm{~m} \) long. Determine the angle of elevation of the sun to the nearest tenth of a degree. 23.7 m high casts a shadow 46.8 m long. Determine the angle of elevation of the sun to the nearest tenth of a degree. Show answer

\( \operatorname{Csc} 82.4^{\circ}= \) Blank 1 Express your answer in 3 decimal points.

\( r = \tan \theta \sec \theta \)

\( \csc 82.4^{\circ}= \) Blank 1 Express your answer in 3 decimal points.