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Hogar Banco de preguntas Matemáticas Trigonometría Archive 2024 December 16

Trigonometry Questions from Dec 16,2024

Browse the Trigonometry Q&A Archive for Dec 16,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Find the exact values of \( \sin 2 \theta, \cos 2 \theta, \tan 2 \theta \) and the quadrant in which \( 2 \theta \) lies. \( \tan \theta=-\frac{15}{8}, \theta \) is in Quadrant II \( \sin 2 \theta=\square \) (Type an integer or a simplified fraction.) 2. A mountain is 780.0 m high. From points \( A \) and \( C \), the angles of elevation to the top of the mountain are \( 67^{\circ} \) and \( 54^{\circ} \) as shown at the left. Explain how to calculate the length of a tunnel from \( A \) to \( C \). Find the exact value of \( \sin 2 \theta, \cos 2 \theta, \tan 2 \theta \), and the quadrant in which \( 2 \theta \) lies \[ \cos \theta=-\frac{28}{53}, \theta \text { in quadrant III } \] 2. A mountain is 780.0 m high. From points \( A \) and \( C \), the angles of elevation to the top of the mountain are \( 67^{\circ} \) and \( 54^{\circ} \) as shown at the left. Explain how to calculate the length of a tunnel from \( A \) to \( C \). igonometric Identities Find the exact value of \( \sin 2 \theta, \cos 2 \theta, \tan 2 \theta \), and the quadrant in which \( 2 \theta \) lies. \[ \cos \theta=-\frac{20}{29}, \theta \text { in quadrant III } \] gonometric Identities Find the exact value of \( \boldsymbol{\operatorname { s i n } 2 \theta , \operatorname { c o s } 2 \theta , \operatorname { t a n } 2 \theta \text { , and the quadrant in which } 2 \theta \text { lies. }} \begin{array}{l}\sin \theta=\frac{48}{73}, \theta \text { in quadrant I } \\ \sin 2 \theta=\square \text { (Type an integer or a simplified fraction.) }\end{array} \) Find an equivalent expression using cofunction identities for the following. \( \tan \left(x+\frac{\pi}{2}\right) \) gonometric Identities Use a sum or difference identity to find the exact value of the expression. \( \tan 15^{\circ} \) Use a sum or difference identity to find the exact value of the expression. \( \cos \frac{5 \pi}{12} \) Factor and simplify. \[ \sin ^{4} x-\cos ^{4} x \]
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