\( f ( x ) = \sin x \quad x = \frac { \pi } { 2 } \)

If \( \sin \theta \) s -0.7660 , which of the following represents an approximate value of \( \tan \theta \), for \( 180^{\circ}<\theta<270^{\circ} \) ? 0.7660 0.8392 1.1916 1.4198

Based on Pythagorean identities, which equation is true? \( \begin{array}{l}\sin ^{2} \theta-1=\cos ^{2} \theta \\ \sec ^{2} \theta-\tan ^{2} \theta=-1 \\ -\cos ^{2} \theta-1=-\sin ^{2} \theta \\ \cot ^{2} \theta-\csc ^{2} \theta=-1\end{array} \)

If \( \tan \theta=-\frac{3}{8} \), which expression is equivalent to \( \cot \theta ? \) \( \frac{1}{-\frac{3}{8}} \) \( -\frac{3}{8}+1 \) \( \sqrt{1+\left(-\frac{\theta}{3}\right)^{2}} \) \( \left(-\frac{3}{8}\right)^{2}+1 \)

Which Pythagorean identity is correct? \( \begin{array}{l}\sin ^{2}(\theta)+1=\cos ^{2}(\theta) \\ \tan ^{2}(\theta)+1=\sec ^{2}(\theta) \\ 1-\cot ^{2}(\theta)=\csc ^{2}(\theta) \\ 1-\cos ^{2}(\theta)=\tan ^{2}(\theta)\end{array} \)

2. Halle el valor numérico de \[ H=2 \cos 180^{\circ} \cdot \sec 360^{\circ} \cdot \csc 270 \] \( \begin{array}{lll}\text { A) }-1 & \text { B) }-2 & \text { C) } 0 \\ \text { D) } 1 & \text { E) } 2 & \end{array} \)