sin kuadrat x cos kuadrat x
Secaraumum terdapat tiga jenis rumus periode yang biasanya kerap digunakan guna menyelesaikan persamaan trigonometri ini, yang diantaranya adalaha: sin x. Yang pertama adalah sin α maka x = α + k.360 dan x. = (180 - α) + k.360. cos x. Yang kedua adalah cos α maka x. = α + k.360. dan x = - α + k.360. tan x.
x= pi/4+ 2k pi, with k in ZZ Oke, I can't come up with anything simpler than this... cosx + sinx = sqrt2 sinx+pi/2 + sinx = sqrt2 Now we know that sina+b + sina-b = 2 sina cosb. To use this equation, we say for example a+b = x+pi/2 a-b = x Solving gives a = x + pi/4 b = pi/4 So now we get sinx+pi/2 + sinx = sina+b + sina-b = 2 sina cosb = 2sinx+pi/4 cospi/4 = 2sinx+pi/4 sqrt2 /2 = sqrt2 sinx+pi/4 Now the equation gets much simpler sinx + sinx+pi/2 = sqrt2 sqrt2 sinx+pi/4 = sqrt2 sinx+pi/4 = 1 x+pi/4 = pi/2 + 2k pi x= pi/4+ 2k pi Where k in ZZ$\begingroup$ I thought this one up, but I am not sure how to solve it. Here is my attempt $$\sin x-\sqrt{3}\ \cos x=1$$ $$\sin x-\sqrt{3}\ \cos x^2=1$$ $$\sin^2x-2\sqrt{3}\sin x\cos x\ +3\cos^2x=1$$ $$1-2\sqrt{3}\sin x\cos x\ +2\cos^2x=1$$ $$2\cos^2x-2\sqrt{3}\sin x\cos x=0$$ $$2\cos x\cos x-\sqrt{3}\sin x=0$$ $2\cos x=0\Rightarrow x\in \{\frac{\pi }22n-1n\in\Bbb Z\}$ But how do I solve $$\cos x-\sqrt{3}\sin x=0$$ asked Nov 10, 2018 at 115 $\endgroup$ 4 $\begingroup$Hint at the very beginning divide both sides by $2$ and use the formula for the sin of difference of 2 arguments answered Nov 10, 2018 at 117 MakinaMakina1,4441 gold badge7 silver badges17 bronze badges $\endgroup$ 1 $\begingroup$ Hint $$\cos x - \sqrt{3}\sin x = 0 \Leftrightarrow \frac{\sin x}{\cos x} = \frac{\sqrt{3}}{3} \Leftrightarrow \tan x = \frac{\sqrt{3}}{3}$$ Note You can divide by $\cos x$, since if the case was $\cos x =0$, it would be $\sin x = \pm 1$ and thus the equation would yield $\pm \sqrt{3} \neq 0$, thus no problems in the final solution, as the $\cos$ zeros are no part of it. answered Nov 10, 2018 at 117 gold badges29 silver badges86 bronze badges $\endgroup$ 8 $\begingroup$ Multiply by the conjugate $\cosx - \sqrt{3} \sinx\cosx + \sqrt{3} \sinx = 0$. Then we have $\cos^2x-3\sin^2x=0$. This is the same thing as $1-4\sin^2x=0$ or $\sinx=\pm \frac{1}{2}$. NOTE OF CAUTION This gives you the answers to both the question and its conjugate. You'd have to plug in and check which ones are the answers you're looking for. answered Nov 10, 2018 at 124 JKreftJKreft2321 silver badge7 bronze badges $\endgroup$ $\begingroup$ You can turn the equation to a polynomial one, $$s-\sqrt3 c=1$$ is rewritten $$s^2=1-c^2=1+\sqrt3c^2,$$ which yields $$c=0\text{ or }c=-\frac{\sqrt3}2.$$ Plugging in the initial equation, $$c=0,s=1\text{ or }c=-\frac{\sqrt3}2,s=-\frac12.$$ Retrieving the angles is easy. answered Nov 10, 2018 at 1025 $\endgroup$ $\begingroup$ It's intersting, I believe, to consider also this other method for solving any linear equation in sine and cosine provided that the argument is the same for both functions. Recall that cosine and sine are abscissa and ordinate of points on the circumference of radius $1$ and center in the origin of the axes. Solving your first equation, therefore, is equivalent to finding the interection points between straight line $$r Y-\sqrt 3 X = 1 $$ and the circumference $$\gamma X^2+Y^2 = 1.$$ This brings you the system $$ \begin{cases} Y-\sqrt 3 X = 1\\ X^2+Y^2 = 1. \end{cases} $$ Replacing $Y = \sqrt 3 X + 1$ in the second equation gives you the quadratic equation $$2X^2 +\sqrt 3 X =0,$$ and, from here, to the solutions $$X_1 = 0, Y_1 = 1$$ and $$\leftX_2 = -\frac{\sqrt 3}{2}, Y_2 = -\frac{1}{2}\right,$$ with a straightforward trigonometric interpretation. I leave you as an exercise to apply the same approach to the equation you propose $$\cos x -\sqrt 3 \sin x = 0.$$ answered Feb 23, 2019 at 2007 dfnudfnu6,4051 gold badge8 silver badges26 bronze badges $\endgroup$ 1 You must log in to answer this question. Not the answer you're looking for? Browse other questions tagged .
2sin2 3x + sin 3x - 1 = 0 untuk 0° ≤ x ≤ 360°. Misalkan sin 3x = p, Jadi himpunan penyelesaiannya adalah {10°, 50°, 90°, 130°, 170°, 210°, 250°, 290°, 330°}Coskuadrat x +sin kuadrat x= - 11017685 wike123 wike123 04.07.2017 Matematika Sekolah Menengah Atas terjawab • terverifikasi oleh ahli Cos kuadrat x +sin kuadrat x= 2 Lihat jawaban Iklan Iklan Pengguna Brainly Pengguna Brainly pakai cara panjangnya, pak, Kalok di kurang berapa jadinya? Iklan
Pembahasan 2 cos2 x + cos x - 1 = 0 untuk 0 ≤ x ≤ 2π. Misalkan cos x = p. Jadi himpunan penyelesaiannya adalah {1/3π, π, 5/3π}