2. El angule \( 60^{\circ} \) equivale en radianes a: \( \begin{array}{ll}\text { A. } \frac{2}{3} \pi \mathrm{rad} & \text { C. } 3 \pi \mathrm{rad} \\ \text { B. } \frac{1}{3} \pi \mathrm{rad}, & \text { D. } \frac{1}{6} \pi \mathrm{rad}\end{array} \)

\( \begin{array}{l}2.1 \text { If } \hat{\mathrm{A}}=310^{\circ} \text { and } \hat{\mathrm{B}}=130,5^{\circ} \text {, determine the following values, correct to ONE } \\ \text { decimal digit: } \\ 2.1 .1 \quad \tan 3 B+\frac{1}{3} \cos \frac{A}{3} \\ 2.1 .2 \quad-\sec \left(\frac{A}{4}-2 B\right) \\ 2.2 \text { If } \cot \theta=-\frac{12}{5} \text { and } \sin \theta>0 \text {, determine the value of } 20 \operatorname{cosec} \theta-12 \sec \theta \text {, } \\ \text { WITHOUT the use of a calculator. } \\ 2.3 \text { Simplify the following expression: } \\ 2.4 \text { Prove that: } \frac{1}{\tan \left(360^{\circ}-x\right) \sec \left(180^{\circ}+x\right) \operatorname{cosec}\left(360^{\circ}+x\right)} \\ 1+\cot ^{2} x\end{array} \frac{1}{1+\tan ^{2} x}=1 \)

Sea \( f(x)=7 \cos \left(x+\frac{\pi}{2}\right)+3 \). Entonces el mínimo valor que puede alcanzar \( f(x) \) es

4. Найдите решения уравнения \( \cos 2 x=2 \cos x-1 \) на отрезке \( \left[-90^{\circ} ; 90^{\circ}\right] \).

2.4 Prove that: \[ \begin{array}{l}\frac{1}{1+\cot ^{2} x}+\frac{1}{1+\tan ^{2} x}=1 \\ 2.5 \text { Solve for } x \text { for } x \in\left[0^{\circ} ; 360^{\circ}\right], \text { correct to ONE decimal digit: } \\ -\frac{2}{3} \sin x+0,524=0\end{array} \]

usa el tecrema del seno para encontrar el angulo opuesto al lado mas pequeño en untriangulo dondé \( a=7, b=10 \), y el angulo opuesto a b es \( 40^{\circ} \)