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Solve the trigonometric equation:
![\mathsf{sin^2\,x-cos^2\,x=0}\qquad\qquad\mathsf{x\in [0,\,2\pi).}\\\\ \mathsf{(1-cos^2\,x)-cos^2\,x=0}\\\\ \mathsf{1-2\,cos^2\,x=0}\\\\ \mathsf{1=2\,cos^2\,x}\\\\ \mathsf{cos^2\,x=\dfrac{1}{2}}](https://tex.z-dn.net/?f=%5Cmathsf%7Bsin%5E2%5C%2Cx-cos%5E2%5C%2Cx%3D0%7D%5Cqquad%5Cqquad%5Cmathsf%7Bx%5Cin%20%5B0%2C%5C%2C2%5Cpi%29.%7D%5C%5C%5C%5C%20%5Cmathsf%7B%281-cos%5E2%5C%2Cx%29-cos%5E2%5C%2Cx%3D0%7D%5C%5C%5C%5C%20%5Cmathsf%7B1-2%5C%2Ccos%5E2%5C%2Cx%3D0%7D%5C%5C%5C%5C%20%5Cmathsf%7B1%3D2%5C%2Ccos%5E2%5C%2Cx%7D%5C%5C%5C%5C%20%5Cmathsf%7Bcos%5E2%5C%2Cx%3D%5Cdfrac%7B1%7D%7B2%7D%7D)
![\mathsf{cos\,x=\pm\,\sqrt{\dfrac{1}{2}}}\\\\\\ \mathsf{cos\,x=\pm\,\dfrac{1}{\sqrt{2}}}\\\\\\ \mathsf{cos\,x=\pm\,\dfrac{1}{\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}}\\\\\\ \mathsf{cos\,x=\pm\,\dfrac{\sqrt{2}}{2}}](https://tex.z-dn.net/?f=%5Cmathsf%7Bcos%5C%2Cx%3D%5Cpm%5C%2C%5Csqrt%7B%5Cdfrac%7B1%7D%7B2%7D%7D%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7Bcos%5C%2Cx%3D%5Cpm%5C%2C%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7Bcos%5C%2Cx%3D%5Cpm%5C%2C%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%5Ccdot%20%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%7B2%7D%7D%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7Bcos%5C%2Cx%3D%5Cpm%5C%2C%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%7D)
![\begin{array}{lcl} \footnotesize\begin{array}{l}\bullet\end{array}~~\mathsf{cos\,x=-\,\dfrac{\sqrt{2}}{2}}&\quad\Rightarrow\quad&\mathsf{x=\pi-\dfrac{\pi}{4}~~or~~x=\pi+\dfrac{\pi}{4}}\\\\ && \mathsf{x=\dfrac{4\pi}{4}-\dfrac{\pi}{4}~~or~~x=\dfrac{4\pi}{4}+\dfrac{\pi}{4}}\\\\ && \mathsf{x=\dfrac{3\pi}{4}~~or~~x=\dfrac{5\pi}{4}}\qquad\quad\checkmark\\\\\\ \footnotesize\begin{array}{l}\bullet\end{array}~~\mathsf{cos\,x=\,\dfrac{\sqrt{2}}{2}}&\quad\Rightarrow\quad&\mathsf{x=\dfrac{\pi}{4}~~or~~x=2\pi-\dfrac{\pi}{4}}\\\\ && \mathsf{x=\dfrac{\pi}{4}~~or~~x=\dfrac{8\pi}{4}-\dfrac{\pi}{4}}\\\\ && \mathsf{x=\dfrac{\pi}{4}~~or~~x=\dfrac{7\pi}{4}}\qquad\quad\checkmark \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Blcl%7D%20%5Cfootnotesize%5Cbegin%7Barray%7D%7Bl%7D%5Cbullet%5Cend%7Barray%7D~~%5Cmathsf%7Bcos%5C%2Cx%3D-%5C%2C%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%7D%26%5Cquad%5CRightarrow%5Cquad%26%5Cmathsf%7Bx%3D%5Cpi-%5Cdfrac%7B%5Cpi%7D%7B4%7D~~or~~x%3D%5Cpi%2B%5Cdfrac%7B%5Cpi%7D%7B4%7D%7D%5C%5C%5C%5C%20%26%26%20%5Cmathsf%7Bx%3D%5Cdfrac%7B4%5Cpi%7D%7B4%7D-%5Cdfrac%7B%5Cpi%7D%7B4%7D~~or~~x%3D%5Cdfrac%7B4%5Cpi%7D%7B4%7D%2B%5Cdfrac%7B%5Cpi%7D%7B4%7D%7D%5C%5C%5C%5C%20%26%26%20%5Cmathsf%7Bx%3D%5Cdfrac%7B3%5Cpi%7D%7B4%7D~~or~~x%3D%5Cdfrac%7B5%5Cpi%7D%7B4%7D%7D%5Cqquad%5Cquad%5Ccheckmark%5C%5C%5C%5C%5C%5C%20%5Cfootnotesize%5Cbegin%7Barray%7D%7Bl%7D%5Cbullet%5Cend%7Barray%7D~~%5Cmathsf%7Bcos%5C%2Cx%3D%5C%2C%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%7D%26%5Cquad%5CRightarrow%5Cquad%26%5Cmathsf%7Bx%3D%5Cdfrac%7B%5Cpi%7D%7B4%7D~~or~~x%3D2%5Cpi-%5Cdfrac%7B%5Cpi%7D%7B4%7D%7D%5C%5C%5C%5C%20%26%26%20%5Cmathsf%7Bx%3D%5Cdfrac%7B%5Cpi%7D%7B4%7D~~or~~x%3D%5Cdfrac%7B8%5Cpi%7D%7B4%7D-%5Cdfrac%7B%5Cpi%7D%7B4%7D%7D%5C%5C%5C%5C%20%26%26%20%5Cmathsf%7Bx%3D%5Cdfrac%7B%5Cpi%7D%7B4%7D~~or~~x%3D%5Cdfrac%7B7%5Cpi%7D%7B4%7D%7D%5Cqquad%5Cquad%5Ccheckmark%20%5Cend%7Barray%7D)
Solution set:
![\mathsf{S=\left\{\dfrac{\pi}{4},\,\dfrac{3\pi}{4},\,\dfrac{5\pi}{4},\,\dfrac{7\pi}{4} \right\}.}](https://tex.z-dn.net/?f=%5Cmathsf%7BS%3D%5Cleft%5C%7B%5Cdfrac%7B%5Cpi%7D%7B4%7D%2C%5C%2C%5Cdfrac%7B3%5Cpi%7D%7B4%7D%2C%5C%2C%5Cdfrac%7B5%5Cpi%7D%7B4%7D%2C%5C%2C%5Cdfrac%7B7%5Cpi%7D%7B4%7D%20%5Cright%5C%7D.%7D)
I hope this helps. =)
Tags: <em>solve trigonometric trig equation sine cosine sin cos identity trigonometry</em>
Answer:
The mean is 4
Step-by-step explanation:
15+2+4 = 21 which you can divide by 3 = 7
<h3>
✰ <u>Solution</u><u> </u><u>:</u><u>-</u></h3>
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1. Here,
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( Linear pair of angles measure upto 180° )
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Thus,
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![\sf \longrightarrow x + 45^\circ = 180^\circ \\ \\ \\ \sf \longrightarrow x = 180^\circ - 45^\circ \\ \\ \\ \sf \longrightarrow \underline{ \boxed{ \frak{ \blue{ x = 135^\circ }}}} \: \star \: \: \: \: \: \: \: \\ \\](https://tex.z-dn.net/?f=%20%5Csf%20%5Clongrightarrow%20x%20%20%2B%2045%5E%5Ccirc%20%3D%20180%5E%5Ccirc%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%20%5Csf%20%5Clongrightarrow%20x%20%3D%20180%5E%5Ccirc%20%20-%2045%5E%5Ccirc%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%5Csf%20%5Clongrightarrow%20%5Cunderline%7B%20%5Cboxed%7B%20%5Cfrak%7B%20%5Cblue%7B%20x%20%3D%20135%5E%5Ccirc%20%7D%7D%7D%7D%20%5C%3A%20%20%5Cstar%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%5C%20%20%5C%5C%20)
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Now, for y,
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( Vertically Opposite Angles)
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Answer:
![y=\frac{1}{2}x+5](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx%2B5)
Step-by-step explanation:
We are given the points (6,8) and (-2,4).
Find the slope:
![m=\frac{4-8}{-2-6}=\frac{-4}{-8}=\boxed{\frac{1}{2}}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B4-8%7D%7B-2-6%7D%3D%5Cfrac%7B-4%7D%7B-8%7D%3D%5Cboxed%7B%5Cfrac%7B1%7D%7B2%7D%7D)
Using a point and the slope, create a point-slope form equation and convert it into slope-intercept.
![y-8=\frac{1}{2}(x-6)\\\\y-8= \frac{1}{2}x-3\\\\y-8+8=\frac{1}{2}x-3+8\\\\\boxed{y=\frac{1}{2}x+5}](https://tex.z-dn.net/?f=y-8%3D%5Cfrac%7B1%7D%7B2%7D%28x-6%29%5C%5C%5C%5Cy-8%3D%20%5Cfrac%7B1%7D%7B2%7Dx-3%5C%5C%5C%5Cy-8%2B8%3D%5Cfrac%7B1%7D%7B2%7Dx-3%2B8%5C%5C%5C%5C%5Cboxed%7By%3D%5Cfrac%7B1%7D%7B2%7Dx%2B5%7D)
Hope this helps!
Answer:
She can't do it, as there is not enough information for that.
Step-by-step explanation:
There is no logical way to do this, and I'm not sure which lesson you are doing