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Home Question Bank Math Trigonometry Archive 2024 December 03

Trigonometry Questions from Dec 03,2024

Browse the Trigonometry Q&A Archive for Dec 03,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 27 feet up. The ladder makes an angle of \( 62^{\circ} \) with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary. Dada la siguiente función trigonométrica \( f(x)=4 \) sen \( \left(-2 x+\frac{7 \pi}{5}\right)-4 \). Se pide: \( \begin{array}{ll}\text { a. Determinar las características de la función } & \text { (2 Ptos) } \\ \text { b. Realizar su gráfica } & \text { (2 Ptos) }\end{array} \) 6. Let \( \theta \) denote the angle between the straight lines with equations \( \frac{x}{a}+\frac{y}{b}=1 \) and \( \frac{x}{a}-\frac{y}{b}=1 \). Then \( \cot \theta= \) (A) \( \infty \) (B) \( \frac{a^{2}-b^{2}}{2 a b} \) (C) \( \frac{2 a b}{a^{2}-b^{2}} \) (D) \( \frac{a^{2}+b^{2}}{2 a b} \) (E) None of the above \( \tan \frac { 5 \pi } { 4 } = \tan 150 ^ { \circ } = ( \frac { - \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } ) \) \( \operatorname { Tan } 150 ^ { \circ } = ( \frac { - \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } ) \) \( \tan 10 x=\cot 5 x \) then \( x= \) ? \( \left. \begin{array} { l } { f ( x ) = \cos ^ { 2 } ( 3 x + \sqrt { x } ) } \\ { f ( x ) = \tan ( x ^ { 2 } + 1 ) ^ { 2 } } \\ { f ( x ) = \frac { \sin x ^ { 2 } } { 1 + \cos 3 x ^ { 2 } } } \end{array} \right. \) 5. Define \( A=\sin ^{2} \theta+\cos ^{4} \theta \). Which of the following is true? (A) \( 1 \leq A \leq 2 \) (B) \( \frac{3}{4} \leq A \leq 1 \) (C) \( \frac{13}{16} \leq A \leq 1 \) (D) \( \frac{3}{4} \leq A \leq \frac{13}{16} \) (E) \( 0 \leq A \leq 1 \) 4. \( \frac{1}{2 \sin 10^{\circ}}-2 \sin 70^{\circ}= \) Find all solution of the equations in the interval \( [0,2 \pi] \) 11. \( 2 \sin x+\sqrt{3}=0 \) 12. \( (\cos x-1)(\sin x+1)=0 \) 13. \( 2 \cos ^{2} t+3 \cos t+1=0 \)
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