Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
52201	Convert to Degrees, Minutes, and Seconds	2.32rad	$2.32$ $2.32$ rad
52202	Verify the Identity	x^2-1=(x-1)(x+1)	$x^{2} - 1 = (x - 1) (x + 1)$ $x^{2} - 1 = (x - 1) (x + 1)$
52203	Find the Reference Angle	sin((3pi)/2)	$sin (\frac{3 π}{2})$ $\sin (\frac{3 π}{2})$
52204	Find Trig Functions Using Identities	tan(theta)=-3/5 , cos(theta)>0	$tan (θ) = - \frac{3}{5}$ $\tan (θ) = - \frac{3}{5}$ , $cos (θ) > 0$ $\cos (θ) > 0$
52205	Find the Cosecant Given the Point	( square root of 7,3)	$(\sqrt{7}, 3)$ $(\sqrt{7}, 3)$
52206	Solve for θ in Degrees	3tan(theta)-2=5tan(theta)-1	$3 tan (θ) - 2 = 5 tan (θ) - 1$ $3 \tan (θ) - 2 = 5 \tan (θ) - 1$
52207	Find the Reference Angle	sin(-pi/3)	$sin (- \frac{π}{3})$ $\sin (- \frac{π}{3})$
52208	Solve for x in Radians	-sin(x)=0	$- sin (x) = 0$ $- \sin (x) = 0$
52209	Find the Value Using the Unit Circle	-( square root of 3)/2	$- \frac{\sqrt{3}}{2}$ $- \frac{\sqrt{3}}{2}$
52210	Find Amplitude, Period, and Phase Shift	y=-4sin(x+3pi) ?	$y = - 4 sin (x + 3 π)$ $y = - 4 \sin (x + 3 π)$ ?
52211	Convert from Radians to Degrees	14rad	$14$ $14$ radians
52212	Find the Cosine of the Angle	300 degrees	$300 °$ $300 °$
52213	Solve for x in Radians	cos(2x)+cos(x)=0	$cos (2 x) + cos (x) = 0$ $\cos (2 x) + \cos (x) = 0$
52214	Find Amplitude, Period, and Phase Shift	y=cos((6pix)/7+pi/2)	$y = cos (\frac{6 π x}{7} + \frac{π}{2})$ $y = \cos (\frac{6 π x}{7} + \frac{π}{2})$
52215	Verify the Identity	sin(3x)=(sin(x))(4cos(x)^2-1)	$sin (3 x) = (sin (x)) (4 {cos}^{2} (x) - 1)$ $\sin (3 x) = (\sin (x)) (4 \cos^{2} (x) - 1)$
52216	Expand the Trigonometric Expression	csc(90 degrees -theta)	$csc (90 ° - θ)$ $\csc (90 ° - θ)$
52217	Find Amplitude, Period, and Phase Shift	y=4+3sin(pi/3x-pi/16)	$y = 4 + 3 sin (\frac{π}{3} x - \frac{π}{16})$ $y = 4 + 3 \sin (\frac{π}{3} x - \frac{π}{16})$
52218	Find Amplitude, Period, and Phase Shift	y=cos(theta-pi)+2	$y = cos (θ - π) + 2$ $y = \cos (θ - π) + 2$
52219	Convert to Rectangular Coordinates	( square root of 3,pi/2)	$(\sqrt{3}, \frac{π}{2})$ $(\sqrt{3}, \frac{π}{2})$
52220	Convert from Degrees to Radians	25deg	$25$ $25$ degrees
52221	Solve for C in Degrees	6cos(C)-4=cos(C)-9	$6 cos (C) - 4 = cos (C) - 9$ $6 \cos (C) - 4 = \cos (C) - 9$
52222	Find the Other Trig Values in Quadrant IV	sec(theta) = square root of 2	$sec (θ) = \sqrt{2}$ $\sec (θ) = \sqrt{2}$
52223	Solve for x in Radians	sin(1/4x)=0	$sin (\frac{1}{4} x) = 0$ $\sin (\frac{1}{4} x) = 0$
52224	Find the Reference Angle	tan((5pi)/3)	$tan (\frac{5 π}{3})$ $\tan (\frac{5 π}{3})$
52225	Verify the Identity	sin(x)tan(x)+cos(x)-sec(x)+1=sec(x)^2cos(x)^2	$sin (x) tan (x) + cos (x) - sec (x) + 1 = {sec}^{2} (x) {cos}^{2} (x)$ $\sin (x) \tan (x) + \cos (x) - \sec (x) + 1 = \sec^{2} (x) \cos^{2} (x)$
52226	Find the Reference Angle	tan((3pi)/2)	$tan (\frac{3 π}{2})$ $\tan (\frac{3 π}{2})$
52227	Expand Using Sum/Difference Formulas	tan(pi+theta)	$tan (π + θ)$ $\tan (π + θ)$
52228	Find Amplitude, Period, and Phase Shift	y=1/4sin((4pix)/7+(2pi)/5)	$y = \frac{1}{4} sin (\frac{4 π x}{7} + \frac{2 π}{5})$ $y = \frac{1}{4} \sin (\frac{4 π x}{7} + \frac{2 π}{5})$
52229	Convert to Trigonometric Form	1-2cos(x)^2+cos(x)^4	$1 - 2 {cos}^{2} (x) + {cos}^{4} (x)$ $1 - 2 \cos^{2} (x) + \cos^{4} (x)$
52230	Convert to Trigonometric Form	cot(theta)+tan(theta)	$cot (θ) + tan (θ)$ $\cot (θ) + \tan (θ)$
52231	Solve for θ in Degrees	4sin(theta)^2=3	$4 {sin}^{2} (θ) = 3$ $4 \sin^{2} (θ) = 3$
52232	Find Trig Functions Using Identities	csc(theta)=4 , cot(theta)<0	$csc (θ) = 4$ $\csc (θ) = 4$ , $cot (θ) < 0$ $\cot (θ) < 0$
52233	Find Trig Functions Using Identities	tan(theta)=24/7 , sin(theta)<0	$tan (θ) = \frac{24}{7}$ $\tan (θ) = \frac{24}{7}$ , $sin (θ) < 0$ $\sin (θ) < 0$
52234	Convert from Radians to Degrees	20rad	$20$ $20$ rad
52235	Find the Other Trig Values in Quadrant III	tan(theta)=0	$tan (θ) = 0$ $\tan (θ) = 0$
52236	Convert from Degrees to Radians	-210deg	$- 210$ $- 210$ degrees
52237	Solve for θ in Degrees	sec(theta)^2-9sec(theta)+20=0	${sec}^{2} (θ) - 9 sec (θ) + 20 = 0$ $\sec^{2} (θ) - 9 \sec (θ) + 20 = 0$
52238	Find Trig Functions Using Identities	sec(t)=2 , sin(t)<0	$sec (t) = 2$ $\sec (t) = 2$ , $sin (t) < 0$ $\sin (t) < 0$
52239	Solve for x in Degrees	8sin(x)cos(x)+cos(x)=0	$8 sin (x) cos (x) + cos (x) = 0$ $8 \sin (x) \cos (x) + \cos (x) = 0$
52240	Find the Length of b	tri{}{}{10}{}{6}{}	 $\begin{matrix} Side & Angle \begin{matrix} b = c = & 10 a = & 6 \end{matrix} & \begin{matrix} A = B = C = \end{matrix} \end{matrix}$ $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = & 10 \\ a = & 6 \end{matrix} & \begin{matrix} A = \\ B = \\ C = \end{matrix} \end{matrix}$
52241	Find the Other Trig Values in Quadrant I	tan(30 degrees )=5/3	$tan (30 °) = \frac{5}{3}$ $\tan (30 °) = \frac{5}{3}$
52242	Find Amplitude, Period, and Phase Shift	y=2cot(1/3x+pi/6)+2	$y = 2 cot (\frac{1}{3} x + \frac{π}{6}) + 2$ $y = 2 \cot (\frac{1}{3} x + \frac{π}{6}) + 2$
52243	Find the Reference Angle	tan((9pi)/4)	$tan (\frac{9 π}{4})$ $\tan (\frac{9 π}{4})$
52244	Find the Reference Angle	sin((11pi)/3)	$sin (\frac{11 π}{3})$ $\sin (\frac{11 π}{3})$
52245	Find Amplitude, Period, and Phase Shift	y=sin(6pix-(4pi)/3)	$y = sin (6 π x - \frac{4 π}{3})$ $y = \sin (6 π x - \frac{4 π}{3})$
52246	Find the Reference Angle	cot((13pi)/3)	$cot (\frac{13 π}{3})$ $\cot (\frac{13 π}{3})$
52247	Solve for θ in Degrees	4csc(theta)^2-25=0	$4 {csc}^{2} (θ) - 25 = 0$ $4 \csc^{2} (θ) - 25 = 0$
52248	Verify the Identity	csc(theta)^2=1+cot(theta)^2	${csc}^{2} (θ) = 1 + {cot}^{2} (θ)$ $\csc^{2} (θ) = 1 + \cot^{2} (θ)$
52249	Find the Cotangent Given the Point	(( square root of 2)/3,-( square root of 7)/3)	$(\frac{\sqrt{2}}{3}, - \frac{\sqrt{7}}{3})$ $(\frac{\sqrt{2}}{3}, - \frac{\sqrt{7}}{3})$
52250	Find the Other Trig Values in Quadrant III	sec(theta)=- square root of 5	$sec (θ) = - \sqrt{5}$ $\sec (θ) = - \sqrt{5}$
52251	Verify the Identity	cos(x)^3sin(x)^2=(sin(x)^2-sin(x)^4)cos(x)	${cos}^{3} (x) {sin}^{2} (x) = ({sin}^{2} (x) - {sin}^{4} (x)) cos (x)$ $\cos^{3} (x) \sin^{2} (x) = (\sin^{2} (x) - \sin^{4} (x)) \cos (x)$
52252	Find Amplitude, Period, and Phase Shift	y=3sin(2x+3pi)-1	$y = 3 sin (2 x + 3 π) - 1$ $y = 3 \sin (2 x + 3 π) - 1$
52253	Find Amplitude, Period, and Phase Shift	f(x)=1/7cot(8theta-120)	$f (x) = \frac{1}{7} cot (8 θ - 120)$ $f (x) = \frac{1}{7} \cot (8 θ - 120)$
52254	Verify the Identity	(cos(x)sin(x))/(cot(x))=1-cos(x)^2	$\frac{cos (x) sin (x)}{cot (x)} = 1 - {cos}^{2} (x)$ $\frac{\cos (x) \sin (x)}{\cot (x)} = 1 - \cos^{2} (x)$
52255	Find Amplitude, Period, and Phase Shift	y=-sin(x/2+pi/3)	$y = - sin (\frac{x}{2} + \frac{π}{3})$ $y = - \sin (\frac{x}{2} + \frac{π}{3})$
52256	Convert from Radians to Degrees	pi/4*180/pi	$\frac{π}{4} \cdot \frac{180}{π}$ $\frac{π}{4} \cdot \frac{180}{π}$
52257	Expand Using Sum/Difference Formulas	1/6(18x-24)	$\frac{1}{6} (18 x - 24)$ $\frac{1}{6} (18 x - 24)$
52258	Convert from Degrees to Radians	320deg	$320$ $320$ degrees
52259	Find the Reference Angle	300deg	$300$ $300$ degrees
52260	Convert from Degrees to Radians	495deg	$495$ $495$ degrees
52261	Solve for θ in Radians	tan(theta)=2sin(theta)	$tan (θ) = 2 sin (θ)$ $\tan (θ) = 2 \sin (θ)$
52262	Find Amplitude, Period, and Phase Shift	y=sin((4x)/3-(5pi)/3)	$y = sin (\frac{4 x}{3} - \frac{5 π}{3})$ $y = \sin (\frac{4 x}{3} - \frac{5 π}{3})$
52263	Find the Secant Given the Point	( square root of 7,3)	$(\sqrt{7}, 3)$ $(\sqrt{7}, 3)$
52264	Find the Cotangent Given the Point	(1/( square root of 2),-1/( square root of 2))	$(\frac{1}{\sqrt{2}}, - \frac{1}{\sqrt{2}})$ $(\frac{1}{\sqrt{2}}, - \frac{1}{\sqrt{2}})$
52265	Find Amplitude, Period, and Phase Shift	y=1/4sin(8pix-(5pi)/4)	$y = \frac{1}{4} sin (8 π x - \frac{5 π}{4})$ $y = \frac{1}{4} \sin (8 π x - \frac{5 π}{4})$
52266	Find the Value Using the Unit Circle	tan(-(7pi)/4)	$tan (- \frac{7 π}{4})$ $\tan (- \frac{7 π}{4})$
52267	Find Amplitude, Period, and Phase Shift	y=2cos((8x)/3-2pi)	$y = 2 cos (\frac{8 x}{3} - 2 π)$ $y = 2 \cos (\frac{8 x}{3} - 2 π)$
52268	Find the Length of b	tri{}{45}{5}{45}{}{90}	 $\begin{matrix} Side & Angle \begin{matrix} b = c = & 5 a = \end{matrix} & \begin{matrix} A = & 45 B = & 45 C = & 90 \end{matrix} \end{matrix}$ $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = & 5 \\ a = \end{matrix} & \begin{matrix} A = & 45 \\ B = & 45 \\ C = & 90 \end{matrix} \end{matrix}$
52269	Find Amplitude, Period, and Phase Shift	y=cos(x-pi/3)+2	$y = cos (x - \frac{π}{3}) + 2$ $y = \cos (x - \frac{π}{3}) + 2$
52270	Expand Using Sum/Difference Formulas	csc(pi/2-x)	$csc (\frac{π}{2} - x)$ $\csc (\frac{π}{2} - x)$
52271	Find the Tangent of the Angle	(5pi)/3	$\frac{5 π}{3}$ $\frac{5 π}{3}$
52272	Find Amplitude, Period, and Phase Shift	y=4cos(-2x-pi/3)	$y = 4 cos (- 2 x - \frac{π}{3})$ $y = 4 \cos (- 2 x - \frac{π}{3})$
52273	Solve for x in Degrees	2sin(x)=1	$2 sin (x) = 1$ $2 \sin (x) = 1$
52274	Solve for X in Degrees	tan(X)=2	$tan (X) = 2$ $\tan (X) = 2$
52275	Solve for x in Degrees	cos(x)sin(x)=-sin(x)	$cos (x) sin (x) = - sin (x)$ $\cos (x) \sin (x) = - \sin (x)$
52276	Verify	sec(x)-tan(x)sin(x)=1/(sec(x))	$sec (x) - tan (x) sin (x) = \frac{1}{sec (x)}$ $\sec (x) - \tan (x) \sin (x) = \frac{1}{\sec (x)}$
52277	Find the Other Trig Values in Quadrant IV	sec(theta) = square root of 3	$sec (θ) = \sqrt{3}$ $\sec (θ) = \sqrt{3}$
52278	Find the Cotangent Given the Point	((- square root of 2)/2,( square root of 2)/2)	$(\frac{- \sqrt{2}}{2}, \frac{\sqrt{2}}{2})$ $(\frac{- \sqrt{2}}{2}, \frac{\sqrt{2}}{2})$
52279	Find Amplitude, Period, and Phase Shift	y=sin(1/6(x+pi/3))	$y = sin (\frac{1}{6} (x + \frac{π}{3}))$ $y = \sin (\frac{1}{6} (x + \frac{π}{3}))$
52280	Convert from Degrees to Radians	250deg	$250$ $250$ degrees
52281	Find Amplitude, Period, and Phase Shift	y=5sec(4x)+10	$y = 5 sec (4 x) + 10$ $y = 5 \sec (4 x) + 10$
52282	Find Amplitude, Period, and Phase Shift	y=1/2cos((6x)/5-1)	$y = \frac{1}{2} cos (\frac{6 x}{5} - 1)$ $y = \frac{1}{2} \cos (\frac{6 x}{5} - 1)$
52283	Find the Reference Angle	cot(210 degrees )	$cot (210 °)$ $\cot (210 °)$
52284	Convert from Radians to Degrees	tan(pi/4)	$tan (\frac{π}{4})$ $\tan (\frac{π}{4})$
52285	Solve for x in Radians	tan(x)=( square root of 3)/2	$tan (x) = \frac{\sqrt{3}}{2}$ $\tan (x) = \frac{\sqrt{3}}{2}$
52286	Find the Cosecant Given the Point	(-( square root of 5)/3,-2/3)	$(- \frac{\sqrt{5}}{3}, - \frac{2}{3})$ $(- \frac{\sqrt{5}}{3}, - \frac{2}{3})$
52287	Find Amplitude, Period, and Phase Shift	y=-2cos(x-pi)-2	$y = - 2 cos (x - π) - 2$ $y = - 2 \cos (x - π) - 2$
52288	Find Amplitude, Period, and Phase Shift	y=1/6sin(x/4)	$y = \frac{1}{6} sin (\frac{x}{4})$ $y = \frac{1}{6} \sin (\frac{x}{4})$
52289	Find Amplitude, Period, and Phase Shift	y=2cos(1/2x)+1	$y = 2 cos (\frac{1}{2} x) + 1$ $y = 2 \cos (\frac{1}{2} x) + 1$
52290	Solve for θ in Degrees	14cos(theta)-5=5cos(theta)-5	$14 cos (θ) - 5 = 5 cos (θ) - 5$ $14 \cos (θ) - 5 = 5 \cos (θ) - 5$
52291	Verify the Identity	(sin(x)^2)/(cos(x))+cos(x)-1/(cos(x))+1=sec(x)^2cos(x)^2	$\frac{{sin}^{2} (x)}{cos (x)} + cos (x) - \frac{1}{cos (x)} + 1 = {sec}^{2} (x) {cos}^{2} (x)$ $\frac{\sin^{2} (x)}{\cos (x)} + \cos (x) - \frac{1}{\cos (x)} + 1 = \sec^{2} (x) \cos^{2} (x)$
52292	Find the Reference Angle	sin((19pi)/6)	$sin (\frac{19 π}{6})$ $\sin (\frac{19 π}{6})$
52293	Solve for x in Radians	sin(x)^2=3cos(x)^2	${sin}^{2} (x) = 3 {cos}^{2} (x)$ $\sin^{2} (x) = 3 \cos^{2} (x)$
52294	Expand Using Sum/Difference Formulas	sin(pi/4+x)	$sin (\frac{π}{4} + x)$ $\sin (\frac{π}{4} + x)$
52295	Convert from Radians to Degrees	1/( square root of 3)	$\frac{1}{\sqrt{3}}$ $\frac{1}{\sqrt{3}}$
52296	Solve for x in Degrees	8cos(x)sin(x)+9sin(x)=0	$8 cos (x) sin (x) + 9 sin (x) = 0$ $8 \cos (x) \sin (x) + 9 \sin (x) = 0$
52297	Solve for x in Radians	2sin(x)^2-3sin(x)=-1	$2 {sin}^{2} (x) - 3 sin (x) = - 1$ $2 \sin^{2} (x) - 3 \sin (x) = - 1$
52298	Solve for θ in Degrees	tan(theta)=-5	$tan (θ) = - 5$ $\tan (θ) = - 5$
52299	Verify the Identity	cot(theta)+1=csc(theta)(cos(theta)+sin(theta))	$cot (θ) + 1 = csc (θ) (cos (θ) + sin (θ))$ $\cot (θ) + 1 = \csc (θ) (\cos (θ) + \sin (θ))$
52300	Solve for θ in Degrees	sec(theta)^2-6sec(theta)+8=0	${sec}^{2} (θ) - 6 sec (θ) + 8 = 0$ $\sec^{2} (θ) - 6 \sec (θ) + 8 = 0$