Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
501	Find the Exact Value	sin(75)-sin(15)	$\sin (75) - \sin (15)$
502	Expand the Trigonometric Expression	2x^2	$2 x^{2}$
503	Expand the Trigonometric Expression	(x-2)^2	${(x - 2)}^{2}$
504	Find the Exact Value	csc(450)	$\csc (450)$
505	Find the Exact Value	sec(-135)	$\sec (- 135)$
506	Find the Exact Value	cos(45-30)	$\cos (45 - 30)$
507	Verify the Identity	(tan(x)-sin(-x))/(1+cos(x))=tan(x)	$\frac{\tan (x) - \sin (- x)}{1 + \cos (x)} = \tan (x)$
508	Verify the Identity	cos(2x)-cos(x)=0	$\cos (2 x) - \cos (x) = 0$
509	Find the Reference Angle	240 degrees	$240 °$
510	Find Amplitude, Period, and Phase Shift	y=4cos(2x)	$y = 4 \cos (2 x)$
511	Find Amplitude, Period, and Phase Shift	y=-3cos(3x)	$y = - 3 \cos (3 x)$
512	Find Amplitude, Period, and Phase Shift	y=-3sin(3x)	$y = - 3 \sin (3 x)$
513	Find Amplitude, Period, and Phase Shift	y=sec(4x)	$y = \sec (4 x)$
514	Find Amplitude, Period, and Phase Shift	y=-5sin(1/2x)	$y = - 5 \sin (\frac{1}{2} x)$
515	Evaluate	natural log of natural log of e^(e^200)	$\ln (\ln (e^{e^{200}}))$
516	Evaluate	log base 8 of 0.25	$\log_{8} (0.25)$
517	Evaluate the Summation	sum from n=3 to 8 of 15-4n	$\sum_{n = 3}^{8} 15 - 4 n$
518	Expand the Logarithmic Expression	log base 2 of (xy)^10	$\log_{2} ({(x y)}^{10})$
519	Expand the Logarithmic Expression	log base 6 of (z/36)^4	$\log_{6} ({(\frac{z}{36})}^{4})$
520	Expand the Logarithmic Expression	natural log of (3x^2)/((x+1)^10)	$\ln (\frac{3 x^{2}}{{(x + 1)}^{10}})$
521	Expand the Logarithmic Expression	log of ( cube root of xy)/(z^2)	$\log (\frac{\sqrt[3]{x y}}{z^{2}})$
522	Expand the Logarithmic Expression	log of (x^3y^4)/(z^6)	$\log (\frac{x^{3} y^{4}}{z^{6}})$
523	Expand the Logarithmic Expression	log of (4x^3)/(y^2(x-1)^5)	$\log (\frac{4 x^{3}}{y^{2} {(x - 1)}^{5}})$
524	Evaluate	log base 0.5 of 4	$\log_{0.5} (4)$
525	Evaluate	log base 2 of 6* log base 6 of 8	$\log_{2} (6) \cdot \log_{6} (8)$
526	Evaluate	log base 2 of 512	$\log_{2} (512)$
527	Evaluate	log base 15 of 14	$\log_{15} (14)$
528	Evaluate	2^( log base 2 of 37)	$2^{\log_{2} (37)}$
529	Evaluate	e^( natural log of square root of 5)	$e^{\ln (\sqrt{5})}$
530	Convert to Rectangular Coordinates	(-7,(2pi)/3)	$(- 7, \frac{2 π}{3})$
531	Convert to Rectangular Coordinates	(3,(5pi)/3)	$(3, \frac{5 π}{3})$
532	Find the Properties	x^2=16y	$x^{2} = 16 y$
533	Find the Properties	x^2=-4y	$x^{2} = - 4 y$
534	Find the Properties	(x^2)/9+(y^2)/16=1	$\frac{x^{2}}{9} + \frac{y^{2}}{16} = 1$
535	Find the Properties	y^2=4x	$y^{2} = 4 x$
536	Find the Properties	2x^2+7y^2=14	$2 x^{2} + 7 y^{2} = 14$
537	Find the Properties	(x^2)/4+(y^2)/9=1	$\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$
538	Find the Properties	(x^2)/16+(y^2)/12=1	$\frac{x^{2}}{16} + \frac{y^{2}}{12} = 1$
539	Find the Properties	(x^2)/16+(y^2)/25=1	$\frac{x^{2}}{16} + \frac{y^{2}}{25} = 1$
540	Find the Properties	(x^2)/25-(y^2)/16=1	$\frac{x^{2}}{25} - \frac{y^{2}}{16} = 1$
541	Solve Using a Matrix with Cramer's Rule	5x+2y-z=1 , x-2y+2z=0 , 2x-3y+z=-2	$5 x + 2 y - z = 1$ , $x - 2 y + 2 z = 0$ , $2 x - 3 y + z = - 2$
542	Find the Properties	9x^2-4y^2=36	$9 x^{2} - 4 y^{2} = 36$
543	Find the Properties	y^2=12x	$y^{2} = 12 x$
544	Find the Properties	x=4y^2	$x = 4 y^{2}$
545	Find the Center and Radius	x^2+y^2-4x+10y+13=0	$x^{2} + y^{2} - 4 x + 10 y + 13 = 0$
546	Simplify/Condense	4 natural log of x-4 natural log of y	$4 \ln (x) - 4 \ln (y)$
547	Find the Vertex Form	(x^2)/4+(y^2)/25=1	$\frac{x^{2}}{4} + \frac{y^{2}}{25} = 1$
548	Find the Vertex Form	x^2+y^2=25	$x^{2} + y^{2} = 25$
549	Find the Vertex Form	9x^2-4y^2=36	$9 x^{2} - 4 y^{2} = 36$
550	Factor over the Complex Numbers	5/2*(cos(150)+isin(150))	$\frac{5}{2} \cdot (\cos (150) + i \sin (150))$
551	Find the Slope	x=-3	$x = - 3$
552	Find the Slope	y=-3	$y = - 3$
553	Determine if Odd, Even, or Neither	f(x)=x^3-5	$f (x) = x^{3} - 5$
554	Determine if Odd, Even, or Neither	f(x) = square root of x	$f (x) = \sqrt{x}$
555	Determine if Odd, Even, or Neither	f(x)=-9x^4+5x+3	$f (x) = - 9 x^{4} + 5 x + 3$
556	Determine if Odd, Even, or Neither	f(x)=cos(x)	$f (x) = \cos (x)$
557	Determine if Odd, Even, or Neither	f(x)=3x^2-1	$f (x) = 3 x^{2} - 1$
558	Graph	x^2=9y	$x^{2} = 9 y$
559	Graph	x^2=5y	$x^{2} = 5 y$
560	Graph	f(x)=2 log base 1/3 of x-1+3	$f (x) = 2 \log_{\frac{1}{3}} (x - 1) + 3$
561	Graph	y^2-(x^2)/9=1	$y^{2} - \frac{x^{2}}{9} = 1$
562	Graph	- log base 3 of x-1+3	$- \log_{3} (x - 1) + 3$
563	Graph	f(x)=-2 log base 1/3 of x-1-1	$f (x) = - 2 \log_{\frac{1}{3}} (x - 1) - 1$
564	Find the Exact Value	cos(195 degrees )	$\cos (195 °)$
565	Graph	r=3sin(x)	$r = 3 \sin (x)$
566	Graph	r=2	$r = 2$
567	Graph	r(x)=6/((x-2)^2)	$r (x) = \frac{6}{{(x - 2)}^{2}}$
568	Expand Using the Binomial Theorem	(sin(x)+cos(x))^2	${(\sin (x) + \cos (x))}^{2}$
569	Evaluate	(25x)/( square root of 125x^3y)	$\frac{25 x}{\sqrt{125 x^{3} y}}$
570	Find the Vertex	y=x^2-2x-3	$y = x^{2} - 2 x - 3$
571	Find the Vertex	y=x^2-6x+5	$y = x^{2} - 6 x + 5$
572	Find the Domain and Range	f(x) = square root of x^2-16	$f (x) = \sqrt{x^{2} - 16}$
573	Evaluate	csc((3pi)/2)	$\csc (\frac{3 π}{2})$
574	Evaluate	sin(75)	$\sin (75)$
575	Evaluate	tan(pi/8)	$\tan (\frac{π}{8})$
576	Expand Using the Binomial Theorem	(3x+y)^5	${(3 x + y)}^{5}$
577	Evaluate	pi/2-pi/4	$\frac{π}{2} - \frac{π}{4}$
578	Evaluate	(2pi)/5	$\frac{2 π}{5}$
579	Simplify/Condense	log base 2 of 6* log base 6 of 8	$\log_{2} (6) \cdot \log_{6} (8)$
580	Simplify/Condense	( log of a)/( log of b)	$\frac{\log (a)}{\log (b)}$
581	Simplify/Condense	e^(3 natural log of x)	$e^{3 \ln (x)}$
582	Simplify/Condense	3 natural log of x+2 natural log of x+1	$3 \ln (x) + 2 \ln (x + 1)$
583	Simplify/Condense	3 log base 3 of x+4 log base 3 of y-4 log base 3 of z	$3 \log_{3} (x) + 4 \log_{3} (y) - 4 \log_{3} (z)$
584	Simplify/Condense	2 natural log of e^6- natural log of e^5	$2 \ln (e^{6}) - \ln (e^{5})$
585	Simplify/Condense	log base 8 of 8x+ log base 8 of 6x^2- log base 8 of 3x^3	$\log_{8} (8 x) + \log_{8} (6 x^{2}) - \log_{8} (3 x^{3})$
586	Simplify/Condense	log base 6 of y-2 log base 6 of z	$\log_{6} (y) - 2 \log_{6} (z)$
587	Find the Center and Radius	x^2+y^2+2x-4y+1=0	$x^{2} + y^{2} + 2 x - 4 y + 1 = 0$
588	Find the Center and Radius	x^2+10x+41+y^2-8y=36	$x^{2} + 10 x + 41 + y^{2} - 8 y = 36$
589	Find the Properties	y=1/8x^2	$y = \frac{1}{8} x^{2}$
590	Find the Properties	x=-1/8y^2	$x = - \frac{1}{8} y^{2}$
591	Find the Properties	((x+3)^2)/144-((y-2)^2)/25=1	$\frac{{(x + 3)}^{2}}{144} - \frac{{(y - 2)}^{2}}{25} = 1$
592	Find the Properties	x^2=-12y	$x^{2} = - 12 y$
593	Find the Properties	x^2-y^2=1	$x^{2} - y^{2} = 1$
594	Find the Center and Radius	(x+3)^2+(y-2)^2=4	${(x + 3)}^{2} + {(y - 2)}^{2} = 4$
595	Find the Center and Radius	(x-4)^2+y^2=16	${(x - 4)}^{2} + y^{2} = 16$
596	Convert to Polar Coordinates	(3,(2pi)/3)	$(3, \frac{2 π}{3})$
597	Convert to Polar Coordinates	(-3 square root of 3,-3)	$(- 3 \sqrt{3}, - 3)$
598	Convert to Polar Coordinates	(2 square root of 3,-2)	$(2 \sqrt{3}, - 2)$
599	Convert to Polar Coordinates	(0,6)	$(0, 6)$
600	Convert to Polar Coordinates	(0,8)	$(0, 8)$