Spencer Griffin
01/07/2023 · Junior High School
4. Trace un triàngulo rectángulo que tenga àngulo agudo \( \theta, y \) encuentre las otras cinco relaciones trigonométricas de \( \theta \). Resolver en hoja aparte. \( \begin{array}{ll}\text { a) } \operatorname{sen} \theta=\frac{3}{5} & \text { d) } \cos \theta=\frac{9}{40} \\ \text { b) } \cot \theta=1 & \text { f) } \tan \theta=\sqrt{3} \\ \text { c) } \sec \theta=\frac{7}{2} & \text { g) } \csc \theta=\frac{13}{12}\end{array} \)
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Para resolver el problema, primero trazaremos un triángulo rectángulo que tenga un ángulo agudo \( \theta \). Luego, utilizaremos las relaciones trigonométricas para encontrar las otras cinco relaciones a partir de las dadas. Relaciones trigonométricas básicas: \( \sin \theta = \frac{a}{c} \), \( \cos \theta = \frac{b}{c} \), \( \tan \theta = \frac{a}{b} \), \( \csc \theta = \frac{c}{a} \), \( \sec \theta = \frac{c}{b} \), \( \cot \theta = \frac{b}{a} \). Resolución de cada caso: a) \( \sin \theta = \frac{3}{5} \), b) \( \cot \theta = 1 \), c) \( \sec \theta = \frac{7}{2} \), d) \( \cos \theta = \frac{9}{40} \), e) \( \tan \theta = \sqrt{3} \), f) \( \csc \theta = \frac{13}{12} \).
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