Find the height of a building that projects a shadow of 350 ft on the ground, If the angle of elevation fr the end of the shadow to the top of the building is \( 40^{\circ} \). a) 234 ft p) 294 ft b) 315 ft d) 302 ft

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

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

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

Three trigonometric functions for a given angle are shown below. \( \sin \theta=-\frac{77}{85}, \cos \theta=\frac{36}{85}, \tan \theta=-\frac{77}{36} \) What are the coordinates of point \( (x, y) \) on the terminal ray of angle \( \theta \), assuming that the values above were not simplified? \( (-77,-36) \) \( (-77,36) \) \( (-36,77) \) \( (36,-77) \)