Angle \( x \) is coterminal with angle \( y \). If the measure of angle \( x \) is greater than the measure of angle \( y \), which statement is true regarding the values of \( x \) and \( y \) ? \( x=y-180 n \), for any positive integer \( n \) \( x=y-360 n \), for any integer \( n \) \( x=y+360 n \), for any positive integer \( n \) \( x=y+180 n \), for any integer \( n \)

Para determinar la altura de un edificio, Carlos se ubica a 10 metros del edificio y mide el ángulo de \( 40^{\circ} \). Si la altura de Carlos es de 1.47 metros, determine la altura del edificio.

value of: \( \frac{\sin \theta+\cos \theta}{2 \sin \theta} \) without using a calculator. \( 4.2 .1 \tan \left(-32^{\circ}\right) \) \( 4.2 .2 \sin 412^{\circ} \) Simplify the following fully and without using a calculator: \( \frac{\sin 120^{\circ} \cdot \tan 300^{\circ}}{\cos \left(-60^{\circ}\right) \cdot \tan 225^{\circ}} \) Prove the following identity: \( \frac{\cos 2 x-\cos x-\sin x}{2 \sin x \cos x+\sin x}=\frac{1}{\tan x}-\frac{1}{\sin x} \) Determine the general solution of: \( \sin (5 \theta)=\cos \left(\theta-40^{\circ}\right) \)

5. Reducir: \[ L=\operatorname{sen} x(\csc x+\operatorname{sen} x)+\cos x(\sec x+\cos x)+1 \] \( \begin{array}{lll}\text { a) } 1 & \text { b) } 2 & \text { c) } 3 \\ \text { d) } 4 & \text { e) } 5 & \text { c) }\end{array} \)

1. Най иите а) \( -9 \cos \alpha ; \) б) \( \sqrt{2} \) tga, если \( \sin \alpha=-\frac{2 \sqrt{2}}{3} \quad \alpha \in\left(\frac{3 \pi}{2} ; 2 \pi\right) \)

\( \left. \begin{array} { l } { \sin x \sin y = \frac { 1 } { 4 } } \\ { \cos x \cos y = \frac { 1 } { 4 } } \end{array} \right. \)