4. Given that \( \sin x=\frac{3}{5} \) and that \( 0<x<\frac{\pi}{2} \), find the exact values of: \( \begin{array}{lll}\text { (a) } \cos x & \text { (b) } \cos 2 x & \text { (c) } \sin 2 x\end{array} \)

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

[6] If \( \cot (90-\theta)=\cot (2 \theta), 0<\theta<90 \), then \( \sin 3 \theta=\ldots \ldots \) (a) 3 (b) 4 (c) 2 (d) 1

3- Sabendo que \( \operatorname{cotag} 40^{\circ}=1,1918 \) e \( \cos 43^{\circ}=0,7314 \), determine. a) \( \operatorname{Cotag} 320^{\circ}= \) b) \( \cos 223^{\circ}= \)

\( \left(\sec 79.36^{\circ}\right)\left(\sin 79.36^{\circ}\right)-\left(\tan 79.36^{\circ}\right)=\underline{\text { Blank } 1} \)

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