\( \cos x= \frac { 5} { 13} \)  Part A: Find \( \sin x \) and \( \tan x \) .   Part B: Sketch two triangles with different side lengths that would have these trigonometric ratios. Label all side lengths.

tan \( 0.8035=\underline{\text { Blank } 1} \) (Express your answer in 3 decimal points) Blank 1 Add your Thnswer

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

(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) \( \cos (X \pm \Delta X) \)

i) \( \frac{\tan \theta \cot \theta}{\sec \theta} \) equals: A \( \sin \theta \)

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