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Trigonometry Questions & Answers

Q:
Use an addition or subtraction formula to write \[ \frac{\tan 39^{\circ}+\tan 24^{\circ}}{1-\tan 39^{\circ} \tan 24^{\circ}} \] as a trigonometric function of one number.
Q:
\( \frac{tan\theta }{tan^{2}\theta -1}=\frac{1}{tan\theta -cot\theta } \)
Q:
\( \frac{tan\theta }{tan^{2}\theta -1}=\frac{1}{tan\theta -cot\theta } \)
Q:
4) \( \operatorname{Si} \tan \Phi=\frac{\sqrt{6}}{3} \), donde " \( \Phi \) " es un ángulo agudo, calcular \( \mathrm{P}=\sqrt{3} \operatorname{Sec} \Phi+\sqrt{2} \operatorname{Csc} \Phi \)
Q:
p. \( \frac{\tan }{\tan ^{2} \theta} \)
Q:
(ii) \( 8^{2}=5^{2}+5^{2}-2(5)(5) \cos \beta \) \( \cos \beta \)
Q:
Given \( B=45^{\circ}, C=75^{\circ} \), and \( a=6 \), use the Law of Sines (if applicable) to find the exact value of \( b \) in triangle \( A B C \).
Q:
Halla los valores de las demás funciones trigonomé- tricas a partir de la función dada, con valores en el primer cuadrante. \( \begin{array}{lll}\text { a. } \tan t=\frac{3 \sqrt{3}}{2} & \text { b. } \cos t=\frac{1}{3} & \text { c. } \operatorname{cosec} t=2 \\ \text { d. } \operatorname{sen} t=\frac{1}{2} & \text { e. } \sec t=3 & \text { cort }=\frac{\sqrt{3}}{3}\end{array} \)
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:
Halla, en cada caso, el valor de las funciones crigo- nométricas a partir de \( P(x, y) \). \( \begin{array}{ll}\text { a. }\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right) & \text { b. }\left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right) \\ \text { c. }\left(\frac{2}{3},-\frac{\sqrt{5}}{3}\right) & \text { d. }\left(\frac{3}{5}, \frac{4}{5}\right)\end{array} \)

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