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Trigonometry

Rank	Topic	Problem	Formatted Problem
52501	Verify the Identity	(tan(theta))/(cot(theta))=tan(theta)^2	$\frac{\tan (θ)}{\cot (θ)} = \tan^{2} (θ)$
52502	Solve for x in Radians	sin(2x)+2cos(x)=0	$\sin (2 x) + 2 \cos (x) = 0$
52503	Solve for x in Radians	sin(1/3x)=0	$\sin (\frac{1}{3} x) = 0$
52504	Find the Reference Angle	csc(-300 degrees )	$\csc (- 300 °)$
52505	Verify the Identity	(x+1)^2=x^2+2x+1	${(x + 1)}^{2} = x^{2} + 2 x + 1$
52506	Find the Other Trig Values in Quadrant I	cos(30 degrees )=( square root of 3)/2	$\cos (30 °) = \frac{\sqrt{3}}{2}$
52507	Find the Reference Angle	cot(-(5pi)/6)	$\cot (- \frac{5 π}{6})$
52508	Find Amplitude, Period, and Phase Shift	y=cos(x/4+pi/4)-2	$y = \cos (\frac{x}{4} + \frac{π}{4}) - 2$
52509	Verify the Identity	1/(cos(t))-cos(t)tan(t)^2=cos(t)	$\frac{1}{\cos (t)} - \cos (t) \tan^{2} (t) = \cos (t)$
52510	Find Amplitude, Period, and Phase Shift	y=cos(pi/18-x/3)+2	$y = \cos (\frac{π}{18} - \frac{x}{3}) + 2$
52511	Find Amplitude, Period, and Phase Shift	y=-1/2cos(x/4+(2pi)/3)-4	$y = - \frac{1}{2} \cos (\frac{x}{4} + \frac{2 π}{3}) - 4$
52512	Find Amplitude, Period, and Phase Shift	f(a)=5/3cos(4/5a)	$f (a) = \frac{5}{3} \cos (\frac{4}{5} a)$
52513	Verify the Identity	(cos(x)-sin(x))/(sin(x)cos(x))=csc(x)-sec(x)	$\frac{\cos (x) - \sin (x)}{\sin (x) \cos (x)} = \csc (x) - \sec (x)$
52514	Expand the Trigonometric Expression	sin((3pi)/2+x)	$\sin (\frac{3 π}{2} + x)$
52515	Convert from Degrees to Radians	540deg	$540$ degrees
52516	Verify the Identity	1/(sec(theta)^2)+1/(csc(theta)^2)=1	$\frac{1}{\sec^{2} (θ)} + \frac{1}{\csc^{2} (θ)} = 1$
52517	Find Amplitude, Period, and Phase Shift	y=1/4cos((3pix)/2-3/5)	$y = \frac{1}{4} \cos (\frac{3 π x}{2} - \frac{3}{5})$
52518	Simplify Using Half-Angle Formula	cos((11pi)/12)	$\cos (\frac{11 π}{12})$
52519	Find the Cotangent Given the Point	(-3/7,(2 square root of 10)/7)	$(- \frac{3}{7}, \frac{2 \sqrt{10}}{7})$
52520	Solve for x in Degrees	3tan(x)sin(x)=sin(x)	$3 \tan (x) \sin (x) = \sin (x)$
52521	Solve for x in Radians	square root of 3cot(x)=-1	$\sqrt{3} \cot (x) = - 1$
52522	Solve for x in Degrees	7sin(x)tan(x)-6tan(x)=0	$7 \sin (x) \tan (x) - 6 \tan (x) = 0$
52523	Solve for θ in Radians	2sin(theta) = square root of 3	$2 \sin (θ) = \sqrt{3}$
52524	Convert from Radians to Degrees	4/(3pi)	$\frac{4}{3 π}$
52525	Convert to Trigonometric Form	cos(pi/3)	$\cos (\frac{π}{3})$
52526	Find Amplitude, Period, and Phase Shift	y=cos(3pix-(2pi)/3)	$y = \cos (3 π x - \frac{2 π}{3})$
52527	Find the Coterminal Angle	-(53pi)/6	$- \frac{53 π}{6}$
52528	Find the Reference Angle	sec(585 degrees )	$\sec (585 °)$
52529	Solve for x in Radians	2sin(x)^2+cos(x)-1=0	$2 \sin^{2} (x) + \cos (x) - 1 = 0$
52530	Verify the Identity	tan(x)=(sec(x))/(csc(x))	$\tan (x) = \frac{\sec (x)}{\csc (x)}$
52531	Solve for θ in Degrees	2cos(theta)-3=5cos(theta)-5	$2 \cos (θ) - 3 = 5 \cos (θ) - 5$
52532	Convert from Radians to Degrees	arcsec(2/( square root of 3))	$arcsec (\frac{2}{\sqrt{3}})$
52533	Convert from Degrees to Radians	-60^o	$- 60^{o}$
52534	Convert from Radians to Degrees	5*180/pi	$5 \cdot \frac{180}{π}$
52535	Solve for θ in Radians	sin(2theta)+cos(theta)=0	$\sin (2 θ) + \cos (θ) = 0$
52536	Find the Secant Given the Point	(-5/9,(2 square root of 14)/9)	$(- \frac{5}{9}, \frac{2 \sqrt{14}}{9})$
52537	Solve for θ in Radians	sec(theta)=undefined	$\sec (θ) = u n d e f i n e d$
52538	Find the Coterminal Angle	-5/4pi	$- \frac{5}{4} π$
52539	Find Amplitude, Period, and Phase Shift	y=3cos(x+(5pi)/6)	$y = 3 \cos (x + \frac{5 π}{6})$
52540	Solve for x in Radians	2sin(x)^2=sin(x)	$2 \sin^{2} (x) = \sin (x)$
52541	Solve for x in Degrees	sin(x)+1=0	$\sin (x) + 1 = 0$
52542	Solve for x in Radians	cos(2x)=-1/2	$\cos (2 x) = - \frac{1}{2}$
52543	Solve for θ in Radians	theta=(-7pi)/4	$θ = \frac{- 7 π}{4}$
52544	Expand the Trigonometric Expression	2sin(10 degrees )cos(10 degrees )	$2 \sin (10 °) \cos (10 °)$
52545	Find the Reference Angle	cos((3pi)/2)	$\cos (\frac{3 π}{2})$
52546	Expand Using Sum/Difference Formulas	(3x+7)(3x-7)	$(3 x + 7) (3 x - 7)$
52547	Solve for x in Radians	sin(2x)-cos(x)=0	$\sin (2 x) - \cos (x) = 0$
52548	Find the Tangent of the Angle	pi/3	$\frac{π}{3}$
52549	Find the Sine of the Angle	pi/3	$\frac{π}{3}$
52550	Solve for θ in Radians	sec((3theta)/2)=-2	$\sec (\frac{3 θ}{2}) = - 2$
52551	Find the Reference Angle	cot(-(10pi)/3)	$\cot (- \frac{10 π}{3})$
52552	Find the Reference Angle	315deg	$315$ degrees
52553	Expand Using Sum/Difference Formulas	a(8+2b-6)	$a (8 + 2 b - 6)$
52554	Convert from Radians to Degrees	arccos(2.3/2.8)	$\arccos (\frac{2.3}{2.8})$
52555	Solve for x in Radians	cos(x)^2=3/4	$\cos^{2} (x) = \frac{3}{4}$
52556	Solve for θ in Degrees	16cos(theta)^2-25=0	$16 \cos^{2} (θ) - 25 = 0$
52557	Find the Secant Given the Point	(3, square root of 2)	$(3, \sqrt{2})$
52558	Solve for θ in Degrees	sin(2theta)-cos(theta)=0	$\sin (2 θ) - \cos (θ) = 0$
52559	Find Amplitude, Period, and Phase Shift	y=3tan(2x+pi)-2	$y = 3 \tan (2 x + π) - 2$
52560	Convert from Radians to Degrees	(5pi)/4*180/pi	$\frac{5 π}{4} \cdot \frac{180}{π}$
52561	Find Amplitude, Period, and Phase Shift	y=-4cos(x-pi/2)+2	$y = - 4 \cos (x - \frac{π}{2}) + 2$
52562	Find the Reference Angle	tan((11pi)/6)	$\tan (\frac{11 π}{6})$
52563	Verify the Identity	1+(tan(theta))/(cot(theta))=sec(theta)^2	$1 + \frac{\tan (θ)}{\cot (θ)} = \sec^{2} (θ)$
52564	Solve for θ in Degrees	2csc(theta)-3=0	$2 \csc (θ) - 3 = 0$
52565	Find the Coterminal Angle	-1323	$- 1323$
52566	Convert from Radians to Degrees	arccos(2.9/3.2)	$\arccos (\frac{2.9}{3.2})$
52567	Solve for θ in Radians	sin(theta)=(- square root of 3)/2	$\sin (θ) = \frac{- \sqrt{3}}{2}$
52568	Find Amplitude, Period, and Phase Shift	y=1/2cos((6pix)/5-1)	$y = \frac{1}{2} \cos (\frac{6 π x}{5} - 1)$
52569	Solve for x in Degrees	9tan(x)sin(x)=10sin(x)	$9 \tan (x) \sin (x) = 10 \sin (x)$
52570	Solve for x in Degrees	8sin(x)tan(x)-7tan(x)=0	$8 \sin (x) \tan (x) - 7 \tan (x) = 0$
52571	Verify the Identity	3x+7=3(x+2)+1	$3 x + 7 = 3 (x + 2) + 1$
52572	Find Amplitude, Period, and Phase Shift	y=2cos(2x+pi)-1	$y = 2 \cos (2 x + π) - 1$
52573	Solve for x in Radians	2sin(x)cos(x) = square root of 2cos(x)	$2 \sin (x) \cos (x) = \sqrt{2} \cos (x)$
52574	Find the Length of c	tri{4}{30}{}{60}{}{90}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = & 4 \\ c = \\ a = \end{matrix} & \begin{matrix} A = & 30 \\ B = & 60 \\ C = & 90 \end{matrix} \end{matrix}$
52575	Convert from Radians to Degrees	arctan(5.6/9.7)	$\arctan (\frac{5.6}{9.7})$
52576	Find the Length of a	tri{9}{30}{}{60}{}{90}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = & 9 \\ c = \\ a = \end{matrix} & \begin{matrix} A = & 30 \\ B = & 60 \\ C = & 90 \end{matrix} \end{matrix}$
52577	Solve for θ in Degrees	4csc(theta)+5=0	$4 \csc (θ) + 5 = 0$
52578	Verify the Identity	sec(x)^6(sec(x)tan(x))-sec(x)^4(sec(x)tan(x))=sec(x)^5tan(x)^3	$\sec^{6} (x) (\sec (x) \tan (x)) - \sec^{4} (x) (\sec (x) \tan (x)) = \sec^{5} (x) \tan^{3} (x)$
52579	Find Amplitude, Period, and Phase Shift	f(x)=sin(2(x-pi/2))+1	$f (x) = \sin (2 (x - \frac{π}{2})) + 1$
52580	Expand Using Sum/Difference Formulas	sin((3pi)/2+theta)	$\sin (\frac{3 π}{2} + θ)$
52581	Solve for x in Degrees	2cos(x)tan(x)=9tan(x)	$2 \cos (x) \tan (x) = 9 \tan (x)$
52582	Convert to Trigonometric Form	cot(theta)sin(theta)	$\cot (θ) \sin (θ)$
52583	Convert from Radians to Degrees	1.5rad	$1.5$ rad
52584	Solve for θ in Degrees	3tan(theta)-2=tan(theta)	$3 \tan (θ) - 2 = \tan (θ)$
52585	Convert from Radians to Degrees	(11pi)/9rad	$\frac{11 π}{9}$ radians
52586	Find the Cosine of the Angle	135	$135$
52587	Verify the Identity	(x+5)^2=x^2+10x+25	${(x + 5)}^{2} = x^{2} + 10 x + 25$
52588	Expand Using Sum/Difference Formulas	x(4x+1)	$x (4 x + 1)$
52589	Find the Length of a	tri{}{45}{2}{45}{}{90}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = & 2 \\ a = \end{matrix} & \begin{matrix} A = & 45 \\ B = & 45 \\ C = & 90 \end{matrix} \end{matrix}$
52590	Find Trig Functions Using Identities	sin(theta)=(2 square root of 5)/5 , cos(theta)=( square root of 5)/5	$\sin (θ) = \frac{2 \sqrt{5}}{5}$ , $\cos (θ) = \frac{\sqrt{5}}{5}$
52591	Solve for x in Radians	csc(x)^2+csc(x)=2	$\csc^{2} (x) + \csc (x) = 2$
52592	Find the Reference Angle	csc(-pi/3)	$\csc (- \frac{π}{3})$
52593	Find Amplitude, Period, and Phase Shift	y=7/8cos((pix)/4)	$y = \frac{7}{8} \cos (\frac{π x}{4})$
52594	Find the Length of a	tri{}{30}{6}{60}{}{90}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = & 6 \\ a = \end{matrix} & \begin{matrix} A = & 30 \\ B = & 60 \\ C = & 90 \end{matrix} \end{matrix}$
52595	Solve for x in Radians	sin(2x) = square root of 2sin(x)	$\sin (2 x) = \sqrt{2} \sin (x)$
52596	Solve for θ in Radians	sin(theta)^2+cos(theta)^2=1	$\sin^{2} (θ) + \cos^{2} (θ) = 1$
52597	Find the Tangent of the Angle	(2pi)/3	$\frac{2 π}{3}$
52598	Verify the Identity	sin(x)=2sin(x/2)cos(x/2)	$\sin (x) = 2 \sin (\frac{x}{2}) \cos (\frac{x}{2})$
52599	Find the Cosine of the Angle	-(2pi)/3	$- \frac{2 π}{3}$
52600	Find Amplitude, Period, and Phase Shift	y=1/4sin(x/6)	$y = \frac{1}{4} \sin (\frac{x}{6})$