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Home Question Bank Math Trigonometry Archive 2024 November 07

Trigonometry Questions from Nov 07,2024

Browse the Trigonometry Q&A Archive for Nov 07,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\[ \begin{array}{l}\text { Solve the equation for } \mathrm{x} \text {, where } \mathrm{x} \text { is restricted to the given interval. } \\ y=9 \cos \mathrm{x}, \text { for } \mathrm{x} \text { in }[0, \pi]\end{array} \] \( \begin{array}{l}\mathrm{x}=\square \\ \text { (Use integers or fractions for any numbers in the expression.) }\end{array} \) स Choose the correct answer below. A. \( \arccos 1=x \) B. \( \arccos (-1)=x \) C. \( \arcsin (-1)=x \) Choose the correct answer below. A. \( \arcsin \left(-\frac{1}{2}\right)=x \) B. \( \arctan \frac{\sqrt{3}}{3}=x \) C. \( \arccos \left(-\frac{1}{2}\right)=x \) 3. Ángulo de elevación de un avión Un avión vuela a una altura de 3000 metros. Desde el suelo, una persona observa el avión con un ángulo de elevación de \( 45^{\circ} \). ¿A qué distancia horizontal se encuentra el avión de la persona? Which one of the following equations has solution \( \frac{3 \pi}{4} ? \) A. \( \arcsin \frac{\sqrt{2}}{2}=x \) B. \( \arccos \left(-\frac{\sqrt{2}}{2}\right)=x \) C. \( \arctan 1=x \) c. \( \frac{\tan ^{2}(\theta)}{\sec \theta}=\sec (\theta)-\cos (\theta) \quad \) d. \( \frac{\sec (\theta)}{\cos (\theta)}-\frac{\tan (\theta)}{\cot (\theta)}=1 \) Which one of the following equations has solution \( \frac{\pi}{4} \) ? Choose the correct answer below. A. \( \arcsin \frac{\sqrt{2}}{2}=x \) B. \( \arctan \frac{\sqrt{3}}{3}=x \) C. \( \arccos \left(-\frac{\sqrt{2}}{2}\right)=x \) Which one of the following equations has solution 0 ? A. \( \arctan 1=\mathrm{x} \) B. \( \arccos 0=\mathrm{x} \) C. \( \arcsin 0=\mathrm{x} \) Q1. Verify (Use known identities e.g., reciprocal, quotient, Pythagorean, even/odd etc. Also see if you can use common denominator, conjugate, or factoring, refer to your guided note) \( \begin{array}{ll}\text { a. }(1+\sin (x)) \cdot(1+\sin (-x))=\cos ^{2}(x) & \text { b. } \frac{\cot (\theta)}{\csc (\theta)}=\cos (\theta)\end{array} \) Hint: Recall \( \sin (-x)=-\sin (x) \) Express the given trigonometric functions in terms of the same function of a positive acute angle. \[ \sin 160^{\circ}, \cos 210^{\circ} \]
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