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TrigonometryQuestion and Answers: Page 1

Question Number 209956 Answers: 0 Comments: 0

Find the maximum value of 7cosA + 24sinA + 32

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If sin x + cos x + tan x + cot x + sec x + csc x = 7 , find sin2x?

$${If}\:{sin}\:{x}\:+\:{cos}\:{x}\:+\:{tan}\:{x}\:+\:{cot}\:{x}\:+ \\ $$$${sec}\:{x}\:+\:{csc}\:{x}\:=\:\mathrm{7}\:,\:{find}\:{sin}\mathrm{2}{x}? \\ $$

Question Number 209822 Answers: 0 Comments: 8

A ramp is supported by six pillars and the talleste on measures 6 meters. The distance between eachi pllar is 5 meters. What will be the height of the third pillar?

$$\mathrm{A}\:\mathrm{ramp}\:\mathrm{is}\:\mathrm{supported}\:\mathrm{by}\:\mathrm{six}\:\mathrm{pillars}\:\mathrm{and}\:\mathrm{the}\:\mathrm{talleste} \\ $$$$\mathrm{on}\:\mathrm{measures}\:\mathrm{6}\:\mathrm{meters}.\:\mathrm{The}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{eachi} \\ $$$$\mathrm{pllar}\:\mathrm{is}\:\mathrm{5}\:\mathrm{meters}.\:\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{height}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{third}\:\mathrm{pillar}?\: \\ $$

Question Number 209781 Answers: 2 Comments: 0

((1+sin 40°−cos 40°)/(1+sin 40°+cos 40°)) =?

$$\:\:\:\frac{\mathrm{1}+\mathrm{sin}\:\mathrm{40}°−\mathrm{cos}\:\mathrm{40}°}{\mathrm{1}+\mathrm{sin}\:\mathrm{40}°+\mathrm{cos}\:\mathrm{40}°}\:=? \\ $$

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In the triangle ABC ; cos(B−C)=(1/3) Show that : ((1−3cos(B+C))/(6sinBcosC))=tanC

$${In}\:{the}\:{triangle}\:{ABC}\:;\:{cos}\left({B}−{C}\right)=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${Show}\:{that}\::\:\:\frac{\mathrm{1}−\mathrm{3}{cos}\left({B}+{C}\right)}{\mathrm{6}{sinBcosC}}={tanC} \\ $$$$ \\ $$

Question Number 209519 Answers: 0 Comments: 3

Is there any n∈N such that sin(n)∈Q ?

$$\mathrm{Is}\:\mathrm{there}\:\mathrm{any}\:{n}\in\mathbb{N}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{sin}\left({n}\right)\in\mathbb{Q}\:? \\ $$

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⋐ π

$$\:\:\:\underbrace{\Subset} \underbrace{ \cancel{} }\pi \\ $$

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determinant ()

Question Number 208252 Answers: 1 Comments: 0

cos (((2π)/(21)))cos (((4π)/(21)))cos (((8π)/(21)))cos (((10π)/(22)))cos (((16π)/(21)))cos (((20π)/(21)))=?

$$\:\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{21}}\right)\mathrm{cos}\:\left(\frac{\mathrm{4}\pi}{\mathrm{21}}\right)\mathrm{cos}\:\left(\frac{\mathrm{8}\pi}{\mathrm{21}}\right)\mathrm{cos}\:\left(\frac{\mathrm{10}\pi}{\mathrm{22}}\right)\mathrm{cos}\:\left(\frac{\mathrm{16}\pi}{\mathrm{21}}\right)\mathrm{cos}\:\left(\frac{\mathrm{20}\pi}{\mathrm{21}}\right)=? \\ $$

Question Number 208130 Answers: 1 Comments: 0

(1/(cos x−cos 3x)) + (1/(cos x−cos 5x)) + (1/(cos x−cos 7x)) + (1/(cos x−cos 11x))=?

$$\:\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{x}−\mathrm{cos}\:\mathrm{3x}}\:+\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{x}−\mathrm{cos}\:\mathrm{5x}}\:+ \\ $$$$\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{x}−\mathrm{cos}\:\mathrm{7x}}\:+\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{x}−\mathrm{cos}\:\mathrm{11x}}=?\: \\ $$

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Question Number 207516 Answers: 2 Comments: 1

3(sinθ − cosθ)^4 + 6(sinθ + cosθ)^2 + 4(sin^6 θ + cos^6 θ) = ?

$$\mathrm{3}\left(\mathrm{sin}\theta\:−\:\mathrm{cos}\theta\right)^{\mathrm{4}} \:+\:\mathrm{6}\left(\mathrm{sin}\theta\:+\:\mathrm{cos}\theta\right)^{\mathrm{2}} \\ $$$$+\:\mathrm{4}\left(\mathrm{sin}^{\mathrm{6}} \theta\:+\:\mathrm{cos}^{\mathrm{6}} \theta\right)\:=\:? \\ $$

Question Number 207434 Answers: 0 Comments: 0

Relating to question 207407 x^3 −12x^2 +27x−17=0 Let x=t+4 t^3 −21t−37=0 The Trigonometric Solution gives these: x_1 =4−2(√7)cos ((π+2sin^(−1) ((37(√7))/(98)))/6) x_2 =4−2(√7)sin ((sin^(−1) ((37(√7))/(98)))/3) x_3 =4+2(√7)sin ((π+sin^(−1) ((37(√7))/(98)))/3) Prove these identities: x_1 =2−((1+2sin (π/(18)))/(2cos (π/9))) x_2 =2+((1+2cos (π/9))/(2cos ((2π)/9))) x_3 =((1+2(√3)sin ((2π)/9))/(2sin (π/(18))))

$$\mathrm{Relating}\:\mathrm{to}\:\mathrm{question}\:\mathrm{207407} \\ $$$${x}^{\mathrm{3}} −\mathrm{12}{x}^{\mathrm{2}} +\mathrm{27}{x}−\mathrm{17}=\mathrm{0} \\ $$$$\mathrm{Let}\:{x}={t}+\mathrm{4} \\ $$$${t}^{\mathrm{3}} −\mathrm{21}{t}−\mathrm{37}=\mathrm{0} \\ $$$$\mathrm{The}\:\mathrm{Trigonometric}\:\mathrm{Solution}\:\mathrm{gives}\:\mathrm{these}: \\ $$$${x}_{\mathrm{1}} =\mathrm{4}−\mathrm{2}\sqrt{\mathrm{7}}\mathrm{cos}\:\frac{\pi+\mathrm{2sin}^{−\mathrm{1}} \:\frac{\mathrm{37}\sqrt{\mathrm{7}}}{\mathrm{98}}}{\mathrm{6}} \\ $$$${x}_{\mathrm{2}} =\mathrm{4}−\mathrm{2}\sqrt{\mathrm{7}}\mathrm{sin}\:\frac{\mathrm{sin}^{−\mathrm{1}} \:\frac{\mathrm{37}\sqrt{\mathrm{7}}}{\mathrm{98}}}{\mathrm{3}} \\ $$$${x}_{\mathrm{3}} =\mathrm{4}+\mathrm{2}\sqrt{\mathrm{7}}\mathrm{sin}\:\frac{\pi+\mathrm{sin}^{−\mathrm{1}} \:\frac{\mathrm{37}\sqrt{\mathrm{7}}}{\mathrm{98}}}{\mathrm{3}} \\ $$$$\mathrm{Prove}\:\mathrm{these}\:\mathrm{identities}: \\ $$$${x}_{\mathrm{1}} =\mathrm{2}−\frac{\mathrm{1}+\mathrm{2sin}\:\frac{\pi}{\mathrm{18}}}{\mathrm{2cos}\:\:\frac{\pi}{\mathrm{9}}} \\ $$$${x}_{\mathrm{2}} =\mathrm{2}+\frac{\mathrm{1}+\mathrm{2cos}\:\frac{\pi}{\mathrm{9}}}{\mathrm{2cos}\:\frac{\mathrm{2}\pi}{\mathrm{9}}} \\ $$$${x}_{\mathrm{3}} =\frac{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{3}}\mathrm{sin}\:\frac{\mathrm{2}\pi}{\mathrm{9}}}{\mathrm{2sin}\:\frac{\pi}{\mathrm{18}}} \\ $$

Question Number 207065 Answers: 1 Comments: 0

f(x)=[cos2x+cos3x][cos4x+cos6x][[cosx+cos5x] evaluar f(((2π)/(13)))

$$ \\ $$$$\:\:\:{f}\left({x}\right)=\left[{cos}\mathrm{2}{x}+{cos}\mathrm{3}{x}\right]\left[{cos}\mathrm{4}{x}+{cos}\mathrm{6}{x}\right]\left[\left[{cosx}+{cos}\mathrm{5}{x}\right]\right. \\ $$$${evaluar}\:\:\:{f}\left(\frac{\mathrm{2}\pi}{\mathrm{13}}\right)\:\: \\ $$

Question Number 206971 Answers: 1 Comments: 0

Construct an angle whose sine is (3/(2 + (√5))) .

$$\mathrm{Construct}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{whose}\:\mathrm{sine}\:\mathrm{is} \\ $$$$\frac{\mathrm{3}}{\mathrm{2}\:+\:\sqrt{\mathrm{5}}}\:. \\ $$

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