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Trigonometry

Rank	Topic	Problem	Formatted Problem
51801	Verify the Identity	cot(theta)+csc(theta)=(sin(theta)+tan(theta))/(sin(theta)tan(theta))	$\cot (θ) + \csc (θ) = \frac{\sin (θ) + \tan (θ)}{\sin (θ) \tan (θ)}$
51802	Verify the Identity	(cot(x))/(tan(x)+cot(x))=cos(x)^2	$\frac{\cot (x)}{\tan (x) + \cot (x)} = \cos^{2} (x)$
51803	Find Trig Functions Using Identities	sin(theta)=-3/4 , cos(theta)>0	$\sin (θ) = - \frac{3}{4}$ , $\cos (θ) > 0$
51804	Find the Cosecant Given the Point	((3 square root of 10)/10,-( square root of 10)/10)	$(\frac{3 \sqrt{10}}{10}, - \frac{\sqrt{10}}{10})$
51805	Convert to Trigonometric Form	1-(cos(x)^2)/(1+sin(x))	$1 - \frac{\cos^{2} (x)}{1 + \sin (x)}$
51806	Convert from Radians to Degrees	(8pi)/3rad	$\frac{8 π}{3}$ rad
51807	Find the Reference Angle	tan((7pi)/6)	$\tan (\frac{7 π}{6})$
51808	Convert to Rectangular Coordinates	(2 square root of 3,pi/3)	$(2 \sqrt{3}, \frac{π}{3})$
51809	Solve for θ in Degrees	cos(theta)^2+2cos(theta)=0	$\cos^{2} (θ) + 2 \cos (θ) = 0$
51810	Convert from Radians to Degrees	(2pi)/3*180/pi	$\frac{2 π}{3} \cdot \frac{180}{π}$
51811	Find Amplitude, Period, and Phase Shift	y=sin(1/2x-pi)	$y = \sin (\frac{1}{2} x - π)$
51812	Convert from Radians to Degrees	pi/8rad	$\frac{π}{8}$ rad
51813	Find the Secant Given the Point	((2 square root of 30)/11,1/11)	$(\frac{2 \sqrt{30}}{11}, \frac{1}{11})$
51814	Find the Cosecant Given the Point	(( square root of 5)/5,-(2 square root of 5)/5)	$(\frac{\sqrt{5}}{5}, - \frac{2 \sqrt{5}}{5})$
51815	Find Amplitude, Period, and Phase Shift	y=1-3cos(3(x-pi/3))	$y = 1 - 3 \cos (3 (x - \frac{π}{3}))$
51816	Find the Cosecant of the Angle	(3pi)/4	$\frac{3 π}{4}$
51817	Solve for B in Degrees	sin(B)=0.4848	$\sin (B) = 0.4848$
51818	Solve for C in Degrees	-cos(C)+6=2cos(C)+6	$- \cos (C) + 6 = 2 \cos (C) + 6$
51819	Verify the Identity	x^2-14x+49=(x-7)^2	$x^{2} - 14 x + 49 = {(x - 7)}^{2}$
51820	Find the Cotangent Given the Point	((3 square root of 13)/13,-(2 square root of 13)/13)	$(\frac{3 \sqrt{13}}{13}, - \frac{2 \sqrt{13}}{13})$
51821	Find the Cosecant Given the Point	(-1, square root of 2)	$(- 1, \sqrt{2})$
51822	Convert from Degrees to Radians	120 degrees *pi/180	$120 ° \cdot \frac{π}{180}$
51823	Find the Reference Angle	210deg	$210$ degrees
51824	Verify the Identity	1+2cot(theta)^2+cot(theta)^4=csc(theta)^4	$1 + 2 \cot^{2} (θ) + \cot^{4} (θ) = \csc^{4} (θ)$
51825	Find Amplitude, Period, and Phase Shift	y=cos(theta-60 degrees )	$y = \cos (θ - 60 °)$
51826	Verify the Identity	x^3-27=(x-3)(x^2+3x+9)	$x^{3} - 27 = (x - 3) (x^{2} + 3 x + 9)$
51827	Convert from Radians to Degrees	sin(1)	$\sin (1)$
51828	Convert to Trigonometric Form	cot(-x)cos(-x)+sin(-x)	$\cot (- x) \cos (- x) + \sin (- x)$
51829	Find the Cosecant Given the Point	((2 square root of 5)/5,-( square root of 5)/5)	$(\frac{2 \sqrt{5}}{5}, - \frac{\sqrt{5}}{5})$
51830	Verify the Identity	sin(x)^3=sin(x)-sin(x)cos(x)^2	$\sin^{3} (x) = \sin (x) - \sin (x) \cos^{2} (x)$
51831	Expand Using Sum/Difference Formulas	csc(90 degrees -theta)	$\csc (90 ° - θ)$
51832	Find the Cosecant Given the Point	(-1/3,(2 square root of 2)/3)	$(- \frac{1}{3}, \frac{2 \sqrt{2}}{3})$
51833	Find Trig Functions Using Identities	tan(theta)=5/12 , cos(theta)<0	$\tan (θ) = \frac{5}{12}$ , $\cos (θ) < 0$
51834	Find the Secant Given the Point	(-3, square root of 3)	$(- 3, \sqrt{3})$
51835	Verify the Identity	1/(tan(x)^2+1)=cos(x)^2	$\frac{1}{\tan^{2} (x) + 1} = \cos^{2} (x)$
51836	Find Trig Functions Using Identities	tan(theta)=4/3 , cos(theta)<0	$\tan (θ) = \frac{4}{3}$ , $\cos (θ) < 0$
51837	Solve for θ in Degrees	sin(theta)=8/10	$\sin (θ) = \frac{8}{10}$
51838	Find the Cotangent Given the Point	(-( square root of 2)/5,( square root of 23)/5)	$(- \frac{\sqrt{2}}{5}, \frac{\sqrt{23}}{5})$
51839	Solve for x in Radians	sin(2x)=- square root of 3sin(x)	$\sin (2 x) = - \sqrt{3} \sin (x)$
51840	Convert from Radians to Degrees	tan(pi/3)	$\tan (\frac{π}{3})$
51841	Find the Tangent Given the Point	((3 square root of 10)/10,-( square root of 10)/10)	$(\frac{3 \sqrt{10}}{10}, - \frac{\sqrt{10}}{10})$
51842	Find the Secant Given the Point	((3 square root of 10)/10,-( square root of 10)/10)	$(\frac{3 \sqrt{10}}{10}, - \frac{\sqrt{10}}{10})$
51843	Convert to Trigonometric Form	sin(theta)+cos(theta)*cot(theta)	$\sin (θ) + \cos (θ) \cdot \cot (θ)$
51844	Find the Reference Angle	tan(765 degrees )	$\tan (765 °)$
51845	Find the Secant Given the Point	(3 1/2,-2 square root of 15)	$(3 \frac{1}{2}, - 2 \sqrt{15})$
51846	Convert from Degrees to Radians	510deg	$510$ degrees
51847	Find the Secant Given the Point	(- square root of 3,-1)	$(- \sqrt{3}, - 1)$
51848	Solve for x in Degrees	3tan(x)^3=tan(x)	$3 \tan^{3} (x) = \tan (x)$
51849	Convert from Degrees to Radians	255deg	$255$ degrees
51850	Find the Cosecant Given the Point	((2 square root of 13)/13,-(3 square root of 13)/13)	$(\frac{2 \sqrt{13}}{13}, - \frac{3 \sqrt{13}}{13})$
51851	Solve for θ in Radians	cos(theta)=-3/5	$\cos (θ) = - \frac{3}{5}$
51852	Find the Secant Given the Point	((2 square root of 5)/5,-( square root of 5)/5)	$(\frac{2 \sqrt{5}}{5}, - \frac{\sqrt{5}}{5})$
51853	Solve for x in Radians	sec(x)=(2 square root of 3)/3	$\sec (x) = \frac{2 \sqrt{3}}{3}$
51854	Find Amplitude, Period, and Phase Shift	f(x)=2*cos(x+pi)	$f (x) = 2 \cdot \cos (x + π)$
51855	Solve for θ in Degrees	tan(theta)^2+5tan(theta)+6=0	$\tan^{2} (θ) + 5 \tan (θ) + 6 = 0$
51856	Find the Secant Given the Point	(1, square root of 3)	$(1, \sqrt{3})$
51857	Solve for θ in Degrees	6csc(theta)+7=0	$6 \csc (θ) + 7 = 0$
51858	Convert from Degrees to Radians	-135deg	$- 135$ degrees
51859	Find Amplitude, Period, and Phase Shift	y=3sin(3pix-(2pi)/3)	$y = 3 \sin (3 π x - \frac{2 π}{3})$
51860	Solve for x in Degrees	3sin(x)^2-sin(x)=1	$3 \sin^{2} (x) - \sin (x) = 1$
51861	Verify the Identity	(1+cot(alpha))/(csc(alpha))=sin(alpha)+cos(alpha)	$\frac{1 + \cot (α)}{\csc (α)} = \sin (α) + \cos (α)$
51862	Verify the Identity	x^4-y^4=(x-y)(x+y)(x^2+y^2)	$x^{4} - y^{4} = (x - y) (x + y) (x^{2} + y^{2})$
51863	Find Amplitude, Period, and Phase Shift	y=2/3sin(pix)	$y = \frac{2}{3} \sin (π x)$
51864	Find the Length of a	tri{4}{30}{}{60}{}{90}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = & 4 \\ c = \\ a = \end{matrix} & \begin{matrix} A = & 30 \\ B = & 60 \\ C = & 90 \end{matrix} \end{matrix}$
51865	Convert from Degrees to Radians	-150deg	$- 150$ degrees
51866	Find the Secant Given the Point	(-1/3,(2 square root of 2)/3)	$(- \frac{1}{3}, \frac{2 \sqrt{2}}{3})$
51867	Find Amplitude, Period, and Phase Shift	y=4sin((8pix)/5-3/2)	$y = 4 \sin (\frac{8 π x}{5} - \frac{3}{2})$
51868	Solve for θ in Degrees	sin(theta)^2+sin(theta)-2=0	$\sin^{2} (θ) + \sin (θ) - 2 = 0$
51869	Find the Reference Angle	120deg	$120$ degrees
51870	Find the Other Trig Values in Quadrant I	cos(60 degrees )=1/2	$\cos (60 °) = \frac{1}{2}$
51871	Find the Coterminal Angle	8pi	$8 π$
51872	Convert from Degrees to Radians	70deg	$70$ degrees
51873	Find the Reference Angle	tan(225 degrees )	$\tan (225 °)$
51874	Find the Reference Angle	13/5pi	$\frac{13}{5} π$
51875	Find the Other Trig Values in Quadrant II	cos(theta)=0	$\cos (θ) = 0$
51876	Find Amplitude, Period, and Phase Shift	y=1+3sin(2(x+pi/2))	$y = 1 + 3 \sin (2 (x + \frac{π}{2}))$
51877	Find the Sine of the Angle	(9pi)/4	$\frac{9 π}{4}$
51878	Find Amplitude, Period, and Phase Shift	y=-4cos(x+6pi)-8	$y = - 4 \cos (x + 6 π) - 8$
51879	Expand Using Sum/Difference Formulas	sin(x+pi)	$\sin (x + π)$
51880	Verify the Identity	(csc(a)+1)/(csc(a)-1)=(1+sin(a))/(1-sin(a))	$\frac{\csc (a) + 1}{\csc (a) - 1} = \frac{1 + \sin (a)}{1 - \sin (a)}$
51881	Solve for x in Degrees	sin(x)=8/10	$\sin (x) = \frac{8}{10}$
51882	Convert to Trigonometric Form	sin(x)^4-cos(x)^4	$\sin^{4} (x) - \cos^{4} (x)$
51883	Solve for θ in Degrees	csc(theta)^2+2csc(theta)-24=0	$\csc^{2} (θ) + 2 \csc (θ) - 24 = 0$
51884	Find Amplitude, Period, and Phase Shift	f(x)=2tan(pi/2x)	$f (x) = 2 \tan (\frac{π}{2} x)$
51885	Find Amplitude, Period, and Phase Shift	y=2sec((2pi)/3+x)+1	$y = 2 \sec (\frac{2 π}{3} + x) + 1$
51886	Find Trig Functions Using Identities	tan(theta)=-3/5 , sin(theta)<0	$\tan (θ) = - \frac{3}{5}$ , $\sin (θ) < 0$
51887	Convert from Degrees to Radians	36deg	$36$ degrees
51888	Find Amplitude, Period, and Phase Shift	y=-7/2tan(x)	$y = - \frac{7}{2} \tan (x)$
51889	Convert from Degrees to Radians	18deg	$18$ degrees
51890	Find the Cosecant Given the Point	(5 1/2,-2 square root of 15)	$(5 \frac{1}{2}, - 2 \sqrt{15})$
51891	Find the Cotangent Given the Point	(5 1/2,-2 square root of 15)	$(5 \frac{1}{2}, - 2 \sqrt{15})$
51892	Convert to Trigonometric Form	(tan(t))/(sec(t)-cos(t))	$\frac{\tan (t)}{\sec (t) - \cos (t)}$
51893	Solve for x in Radians	3tan(x)^3=tan(x)	$3 \tan^{3} (x) = \tan (x)$
51894	Find Amplitude, Period, and Phase Shift	y=sin(x/2+pi/3)	$y = \sin (\frac{x}{2} + \frac{π}{3})$
51895	Expand Using Sum/Difference Formulas	tan(u-pi/4)	$\tan (u - \frac{π}{4})$
51896	Find the Other Trig Values in Quadrant III	cos(theta)=-0.8	$\cos (θ) = - 0.8$
51897	Find Trig Functions Using Identities	sin(theta)=(2 square root of 2)/3 , cos(theta)=-1/3	$\sin (θ) = \frac{2 \sqrt{2}}{3}$ , $\cos (θ) = - \frac{1}{3}$
51898	Find the Other Trig Values in Quadrant II	sec(theta)=-1	$\sec (θ) = - 1$
51899	Convert from Degrees to Radians	-90deg	$- 90$ degrees
51900	Verify the Identity	(cos(x))(tan(x)+sin(x)cot(x))=sin(x)+cos(x)^2	$(\cos (x)) (\tan (x) + \sin (x) \cot (x)) = \sin (x) + \cos^{2} (x)$