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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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Solve the equation for exact solutions over the linterval \( [0,2 \pi) \). 7 tan \( 3 x=7 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \{ \). Type an exact answer, using \( \pi \) as needed. Type your answer in radians Use integers or fractio for any numbers in the expression. Use a comma to separate answers as needed.) B. The solution is the empty set. Two sides and an angle are given below. Determine whether the given information results in one triangle, two triangles, or no triangle at all, Solve any resulting triangle(s). \[ b=6, c=7, B=30^{\circ} \] Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Type an integer or decimal rounded to two decimal places as needed.) To get a good view of a person in front of a teller's window, it is deter figure to the right. At what angle of depression should the camera be What is the angle of depression? A \( \approx \square^{\circ} \) I (Do not round until the final answer. Then round to the nearest tenth 9. En un triángulo rectángulo se cumple que la diferencia de las medidas de la hipotenusa con uno de los catetos es 8 y con el otro es 9 , calcular el valor de la tangente del mayor ángulo de dicho triángulo. Solve the equation for exact solutions over the interval \( \left[0,360^{\circ}\right) \), \( \sin (3 \theta)=-1 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \{ \}. (Simplify your answer. Type your answer in degrees. Do not include the degree symbol in your answer. Use a comma to separate answers as needed.) B. The solution is the empty set. account for \( 10 \% \) of your grade. (Use your pre-class guided note) 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) \( \begin{array}{ll}\text { a. }(1+\sin (x)) \cdot(1+\sin (-x))=\cos ^{2}(x) & \text { b. } \frac{\cot (\theta)}{\csc (\theta)}=\cos (\theta) \\ \text { Hint: } \operatorname{Recall} \sin (-x)=-\sin (x) & \\ \text { c. } \frac{\tan ^{2}(\theta)}{\sec \theta}=\sec (\theta)-\cos (\theta) & \text { d. } \frac{\sec (\theta)}{\cos (\theta)}-\frac{\tan (\theta)}{\cot (\theta)}=1\end{array} \) \( 1 \leftarrow \quad \) Solve the equation for \( x \), where \( x \) is restricted to the given interval. \[ y=8 \sec 3 x \text {, for } x \text { in }\left[0, \frac{\pi}{6}\right) \cup\left(\frac{\pi}{6}, \frac{\pi}{3}\right] \] account for \( 10 \% \) of your grade. (Use your pre-class guided note) 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) \( \begin{array}{ll}\text { a. }(1+\sin (x)) \cdot(1+\sin (-x))=\cos ^{2}(x) & \text { b. } \frac{\cot (\theta)}{\csc (\theta)}=\cos (\theta) \\ \text { Hint: Recall } \sin (-x)=-\sin (x) & \\ \begin{array}{ll}\tan ^{2}(\theta) \\ \sec \theta\end{array} \sec (\theta)-\cos (\theta) & \text { d. } \frac{\sec (\theta)}{\cos (\theta)}-\frac{\tan (\theta)}{\cot (\theta)}=1\end{array} \) \( f=9 \cos x \), for \( x \) in \( [0, \pi] \) c. \( \frac{\tan ^{2}(\theta)}{\sec \theta}=\sec (\theta)-\cos (\theta) \quad \) d. \( \frac{\sec (\theta)}{\cos (\theta)}-\frac{\tan (\theta)}{\cot (\theta)}=1 \)
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