8. ( 9 points) An architectural team is designing a stairway for an office building. The steep angle of the main stairway is designed to form an angle \( \theta \) with the ground. To create a more accessible stairway for visitors, they plan to design an alternate stairway with half the steepness of the main one. If the steep angle of the main stairway is such that \( \tan (\theta)=7 / 4 \), what is the measurement of the angle for the more accessible stairway?

5. Grafica las siguientes funciones en hojas milimetradas y luego verifica con geogebra. a. \( -4 \operatorname{sen} x \) b. \( \operatorname{Sen} 4 x+2 \) c. \( 3 \cos 2 x+1 \) d. \( 2 \operatorname{sen} 3 x-1 \)

5. Grafica las siguientes funciones en hojas milimetradas y luego verifica con geogebra. a. \( -4 \operatorname{sen} x \) b. \( \operatorname{Sen} 4 x+2 \) c. \( 3 \cos 2 x+1 \) d. \( 2 \operatorname{sen} 3 x-1 \)

\( \sin (+\cos (\frac{\pi }{6}))-\cos (x\times \sin (\frac{\pi }{6}))\leq \frac{1}{2} \)

Find all solutions to the equation. \[ \sin \left(x+\frac{\pi}{3}\right)+\sin \left(x-\frac{\pi}{3}\right)=1 \] Write your answer in radians in terms of \( \pi \), and use the or button as necessary. Example: \( x=\frac{\pi}{5}+2 k \pi, k \in \mathbb{Z} \) or \( x=\frac{\pi}{7}+k \pi, k \in \mathbb{Z} \)

Find all solutions to the equation. \[ \tan 3 x+\sqrt{3}=0 \] Write your answer in radians in terms of \( \pi \), and use the "or" button as necessary. Example: \( x=\frac{\pi}{5}+2 k \pi, k \in \mathbb{Z} \) or \( x=\frac{\pi}{7}+k \pi, k \in \mathbb{Z} \)