Tema
Q:
Question
A boat is heading towards a lighthouse, whose beacon-light is 103 feet above the water. From
point \( A \), the boat's crew measures the angle of elevation to the beacon, \( 6^{\circ} \), before they draw
closer. They measure the angle of elevation a second time from point \( B \) at some later time to be
11. Find the distance from point \( A \) to point \( B \). Round your answer to the nearest tenth of a foot
if necessary.
Q:
NIVEL: AVANZADO
7) En un triángulo rectángulo \( \mathrm{ABC}\left(\mathrm{m} \angle \mathrm{C}=90^{\circ}\right) \) se cumple que:
\( \frac{\operatorname{Cos} \mathrm{A}}{\operatorname{CosB}}=\frac{7}{2} \). Calcular: \( \mathrm{P}=49 \sec \mathrm{~A} \cdot \cot \mathrm{~B} \)
Q:
mopp/student/3403437/23887072/782fc4b23512a429603c9...
Question
A boat is heading towards a lighthouse, whose beacon-light is 103 feet above the water. From
point \( A \), the boat's crew measures the angle of elevation to the beacon, \( 6^{\circ} \), before they draw
closer. They measure the angle of elevation a second time from point \( B \) at some later time to be
\( 11^{\circ} \). Find the distance from point \( A \) to point \( B \). Round your answer to the nearest tenth of a foot
if necessary.
Q:
Representa, en cada caso, el ángulo \( t \) en posición
normal y encuentra el valor de las funciones trigo-
nométricas seno, coseno \( y \) tangente.
\( \begin{array}{lll}\text { a. } t=\frac{3 \pi}{2} & \text { b. } t=2 \pi & \text { c. } t=\frac{\pi}{2} \\ \text { d. } t=\frac{2 \pi}{3} & \text { e. } t=\frac{\pi}{6} & \text { f. } t=-\frac{\pi}{6}\end{array} \)
Q:
Rewrite \( \cos \left(x+\frac{\pi}{3}\right) \) in terms of \( \sin (x) \) and \( \cos (x) \). You answer should not have \( \frac{\pi}{3} \) in it.
Q:
4. Given that \( \sin x=\frac{3}{5} \) and that \( 0<x<\frac{\pi}{2} \), find the exact values of:
\( \begin{array}{lll}\text { (a) } \cos x & \text { (b) } \cos 2 x & \text { (c) } \sin 2 x\end{array} \)
Q:
3. Prove each co-function identity using the compound angle identities.
(a) \( \tan \left(\frac{\pi}{2}-\theta\right)=\cot \theta \)
(b) \( \sin \left(\frac{\pi}{2}-\theta\right)=\cos \theta \)
(c) \( \csc \left(\frac{\pi}{2}-\theta\right)=\sec \theta \)
4. Given that \( \sin x=\frac{3}{5} \) and that \( 0<x<\frac{\pi}{2} \), find the exact values of:
Q:
(1) Halla, en cada caso, el valor de las funciones trigo-
nométricas a partir de \( P(x, y) \).
\( \begin{array}{ll}\text { a. }\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right) & \text { b. }\left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right) \\ \text { c. }\left(\frac{2}{3},-\frac{\sqrt{5}}{3}\right) & \text { d. }\left(\frac{3}{5}, \frac{4}{5}\right)\end{array} \)
Q:
2. Sketch a standard position angle with each radian
measure.
\( \begin{array}{lll}\text { a. } \frac{5 \pi}{4} & \text { b. }-\pi \\ \text { c. } \frac{-4 \pi}{3} & \text { d. } \frac{15 \pi}{4}\end{array} \)
Convert to degrees, minutes, and seconds (DMS).
\( \begin{array}{lll}\text { 3. }-2.87^{\circ} & \text { 4. } 110.51^{\circ} & \text { 5. } 48.362^{\circ}\end{array} \)
Convert to decimal degrees (DD).
\( \begin{array}{lll}\text { 6. }-58^{\circ} 54^{\prime} & \text { 7. } 98^{\circ} 45^{\prime} 43.2^{\prime \prime} & \text { 8. } 135^{\circ} 35^{\prime} 38.4^{\prime \prime}\end{array} \)
Q:
En los ejercicios 1 a 5 encuentre las soluciones de
la ecuación en el intervalo \( 0^{\circ} \leq \theta \leq 360^{\circ} \)
1. \( \operatorname{sen} \theta=\frac{\sqrt{3}}{2} \)
2. \( \cos \theta-1=0 \)
3. \( \tan \theta+\sqrt{3}=0 \)
4. \( \sec \theta-\sqrt{2}=0 \)
5. \( \cot \theta=-1 \)
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