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Home Question Bank Math Trigonometry Archive 2025 January 15

Trigonometry Questions from Jan 15,2025

Browse the Trigonometry Q&A Archive for Jan 15,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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What are the coordinates of the terminal point determined by \( t=\frac{20 \pi}{3} \) ? \[ \text { A. }\left(-\frac{1}{2}, \frac{\sqrt{3}}{2}\right) \] B. \( \left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right) \) C. \( \left(-\frac{1}{2},-\frac{\sqrt{3}}{2}\right) \) D. \( \left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right) \) If \( \sin \theta=\frac{2}{3} \), which of the following are possible for the same value of \( \theta \) ? \( \square \) A. \( \cos \theta=-\frac{\sqrt{5}}{3} \) and \( \tan \theta=\frac{2}{\sqrt{5}} \) \( \square \) B. \( \cos \theta=\frac{\sqrt{5}}{3} \) and \( \tan \theta=\frac{2}{\sqrt{5}} \) \( \square \) C. \( \sec \theta=\frac{3}{\sqrt{5}} \) and \( \tan _{\theta}=\frac{2}{\sqrt{5}} \) \( \square \) D. \( \sec _{\theta}=-\frac{3}{2} \) and \( \tan \theta=\frac{2}{\sqrt{5}} \) c) \( \tan x<0 \) and \( 180^{\circ}<x<360^{\circ} \) d) \( \cos x>0 \) and \( \sin x<0 \) ? (d) If \( 12 \tan \mathrm{C}+5=0 \) and C C \( \left(90^{\circ} ; 270^{\circ}\right) \), find the value of \( 12 \tan \mathrm{C}-13 \cos \mathrm{C} \) wit the aid of a diagram and without using a calculator. (5) Given that \( \sin \alpha=-\frac{3}{5} \) and \( \cos \alpha>0 \), determine, without the the of a calculator, the value of \( 12 \tan a+15 \cos a \). b. If \( O A \) is 6 units, \( A \) is the point \( (-\sqrt{11} ; y) \) and \( X O A=\alpha \), use the given diagram calculate the value of: b) \( \sin \alpha-\sqrt{11} \cos \alpha \) \( \operatorname{Sin} \) GPP c) \( \tan x<0 \) and \( 180^{\circ}<x<360^{\circ} \) d) \( \cos x>0 \) and \( \sin x<0 \) ? (d) If \( 12 \tan \mathrm{C}+5=0 \) and C C \( \left(90^{\circ} ; 270^{\circ}\right) \), find the value of \( 12 \tan \mathrm{C}-13 \cos \mathrm{C} \) wit the aid of a diagram and without using a calculator. (5) Given that \( \sin \alpha=-\frac{3}{5} \) and \( \cos \alpha>0 \), determine, without the the of a calculator, the value of \( 12 \tan a+15 \cos a \). b. If \( O A \) is 6 units, \( A \) is the point \( (-\sqrt{11} ; y) \) and \( X O A=\alpha \), use the given diagram calculate the value of: b) \( \sin \alpha-\sqrt{11} \cos \alpha \) \( \operatorname{Sin} \) GPP c) \( \tan x<0 \) and \( 180^{\circ}<x<360^{\circ} \) d) \( \cos x>0 \) and \( \sin x<0 \) ? (d) If \( 12 \tan \mathrm{C}+5=0 \) and C C \( \left(90^{\circ} ; 270^{\circ}\right) \), find the value of \( 12 \tan \mathrm{C}-13 \cos \mathrm{C} \) wit the aid of a diagram and without using a calculator. (5) Given that \( \sin \alpha=-\frac{3}{5} \) and \( \cos \alpha>0 \), determine, without the the of a calculator, the value of \( 12 \tan a+15 \cos a \). b. If \( O A \) is 6 units, \( A \) is the point \( (-\sqrt{11} ; y) \) and \( X O A=\alpha \), use the given diagram calculate the value of: b) \( \sin \alpha-\sqrt{11} \cos \alpha \) \( \operatorname{Sin} \) GPP What is the value of x if \( \tan^{-1}(x) = 1 \)? \( 3 \cos \theta+3=4 \sin ^{2} \theta \). Find the general solution. \( \sin \left(\theta-20^{\circ}\right)=\cos 3 \theta \). Find the general solution. \( \tan \left(\theta+40^{\circ}\right)=\tan 52^{\circ} \) and \( -360^{\circ} \leq \theta \leq 360^{\circ} \) \( 3 \cos \theta+3=4 \sin ^{2} \theta \). Find the general solution.
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