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11. The general solutions to the trigonometric equation can be written in the form, - \( x=\frac{a \pi}{b}+n 2 \pi, n \varepsilon I \) - \( x=\frac{c \pi}{b}+n 2 \pi, n \varepsilon I \) - \( x=d \pi+n 2 \pi, n \varepsilon I \) Record the values of \( a, b, c \) and \( d \) as a four digit number, in that order. Your answer:

Ask by Fitzgerald Parry. in Canada
Jan 11,2025

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Cannot determine the values of \( a \), \( b \), \( c \), and \( d \) without the specific trigonometric equation.

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Bonus Knowledge

To solve the trigonometric equation, we need to determine the values of \( a \), \( b \), \( c \), and \( d \) from the general solutions provided. Let's consider a standard trigonometric equation like \( \sin(x) = 0 \). For \( \sin(x) = 0 \), the solutions are \( x = n\pi \), where \( n \in \mathbb{Z} \). In comparing this to the provided forms: - For \( x = n\pi \), we can write it as \( x = d\pi + n 2\pi \), where \( d = 0 \). - In \( x=\frac{a \pi}{b}+n 2 \pi \) and \( x=\frac{c \pi}{b}+n 2 \pi \), we can assume \( a = 0 \) and \( b = 1 \) for the simplest rational form. Thus, \( a = 0 \), \( b = 1 \), \( c = 0 \), and \( d = 0 \). Recording these values as a four-digit number: **0000**.

Related Questions

8. Simplify without using a calculator. (8.1) \( \frac{\sin \left(180^{\circ}-x\right) \cdot \tan \left(360^{\circ}-x\right)}{\cos \left(80^{\circ}-x\right)} \times \frac{\cos \left(-180^{\circ}-x\right)}{\cos \left(360^{\circ}+x\right) \sin \left(360^{\circ}-x\right)} \) \( 8.2 \frac{\cos 135^{\circ} \sin 160^{\circ}}{\sin 225^{\circ} \cos 70^{\circ}} \) (8.3) \( \frac{\sin (-\theta)+\cos 120^{\circ}+\tan \left(-180^{\circ}-\theta\right)}{\sin ^{2} 225^{\circ}-\tan (-\theta)-\cos \left(90^{\circ}+\theta\right)} \) B.4 \( 4^{x} \frac{\sin 247^{\circ} \cdot \tan 23^{\circ} \cdot \cos 113^{\circ}}{\sin \left(-157^{\circ}\right)} \) (8.5) \( \frac{3 \cos 150^{\circ} \cdot \sin 270^{\circ}}{\tan \left(-45^{\circ}\right) \cdot \cos 600^{\circ}} \) 8.6) \( \frac{\tan \left(180^{\circ}-x\right) \cdot \sin \left(90^{\circ}+x\right)}{\sin (-x)}-\sin y \cdot \cos \left(90^{\circ}-y\right) \) \( 8.7 \frac{\tan 30^{\circ} \cdot \sin 60^{\circ} \cdot \cos 25^{\circ}}{\cos 135^{\circ} \cdot \sin \left(-45^{\circ}\right) \cdot \sin 65^{\circ}} \) 6.8) \( \frac{\tan \left(180^{\circ}-x\right) \cdot \sin \left(90^{\circ}-x\right)}{\cos \left(90^{\circ}+x\right)}-\frac{\cos \left(180^{\circ}-x\right)}{\sin \left(90^{\circ}+x\right)} \) \( 8.9 \frac{\sin 189^{\circ}}{\tan 549^{\circ}}-\frac{\cos ^{2}\left(-9^{\circ}\right)}{\sin 99^{\circ}} \) Solving trigonometric equations (no calculators) (1.) If \( \sin \mathrm{A}=\frac{-3}{5} \) and \( 0^{\circ}<\mathrm{A}<270^{\circ} \) determine the value of: \( 1.1 \cos A \) \( 1.2 \tan A \). (2.) If \( -5 \tan \theta-3=0 \) and \( \sin \theta<0 \), determine: \( 2.1 \sin ^{2} \theta^{\circ} \) \( 2.25 \cos \theta \) \( 2.3 \quad 1-\cos ^{2} \theta \) 3. If \( 13 \cos \theta+12=0 \) and \( 180^{\circ}<\theta<360^{\circ} \), evaluate: \( 3.2 \tan \theta \) \( 3.1 \sin \theta \cos \theta \) \( 3.3 \sin ^{2} \theta+\cos ^{2} \theta \). (4.) If \( 3 \tan \theta-2=0 \) and \( \theta \in\left[90^{\circ} ; 360^{\circ}\right] \), determine, the value of \( \sqrt{13}(\sin \theta-\cos \theta \) (5.) If \( \cos 52^{\circ}=k \) as illustrated in the diagram, determine each of the following i
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