Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
40601	Find the x and y Intercepts	p(x)=-1/2x^3+3/2x-1	$p (x) = - \frac{1}{2} x^{3} + \frac{3}{2} x - 1$
40602	Find the Value Using the Unit Circle	-pi/6	$- \frac{π}{6}$
40603	Find the Domain	square root of x^2-81	$\sqrt{x^{2} - 81}$
40604	Verify the Identity	sec(theta)-cos(theta)=tan(theta)sin(theta)	$\sec (θ) - \cos (θ) = \tan (θ) \sin (θ)$
40605	Verify the Identity	cos(pi/2-theta)=sin(theta)	$\cos (\frac{π}{2} - θ) = \sin (θ)$
40606	Convert to Trigonometric Form	12-12i	$12 - 12 i$
40607	Find the x and y Intercepts	x^2+y^2-8x-4y-16=0	$x^{2} + y^{2} - 8 x - 4 y - 16 = 0$
40608	Find Amplitude, Period, and Phase Shift	y=-2tan(x)	$y = - 2 \tan (x)$
40609	Find Amplitude, Period, and Phase Shift	y=9sin(pix)	$y = 9 \sin (π x)$
40610	Evaluate the Difference Quotient	(f(x+h)-f(x))/h , f(x)=9x^2+4	$\frac{f (x + h) - f (x)}{h}$ , $f (x) = 9 x^{2} + 4$
40611	Find Trig Functions Using Identities	sin(2theta)=-1/2	$\sin (2 θ) = - \frac{1}{2}$
40612	Find Trig Functions Using Identities	(sin(theta)+cos(theta))^2+(sin(theta)-cos(theta))^2	${(\sin (θ) + \cos (θ))}^{2} + {(\sin (θ) - \cos (θ))}^{2}$
40613	Divide	180/15	$\frac{180}{15}$
40614	Divide	315/180	$\frac{315}{180}$
40615	Divide	14/4	$\frac{14}{4}$
40616	Convert to Rectangular Coordinates	(-3,-60 degrees )	$(- 3, - 60 °)$
40617	Convert to Rectangular Coordinates	(6,120 degrees )	$(6, 120 °)$
40618	Convert to Rectangular Coordinates	(2,60 degrees )	$(2, 60 °)$
40619	Find the Trig Value	cos(theta/2)	$\cos (\frac{θ}{2})$
40620	Find the Trig Value	sin(theta)=4/5 , 90 degrees <theta<180 degrees	$\sin (θ) = \frac{4}{5}$ , $90 ° < θ < 180 °$
40621	Find the Domain and Range	g(x)=2^x-2	$g (x) = 2^{x} - 2$
40622	Find the Domain	f(x) = square root of x^2-144	$f (x) = \sqrt{x^{2} - 144}$
40623	Find the Domain	g(x) = square root of 5-10x	$g (x) = \sqrt{5 - 10 x}$
40624	Find the Domain and Range	y=sin(-5x)	$y = \sin (- 5 x)$
40625	Convert from Degrees to Radians	-350 degrees	$- 350 °$
40626	Factor	cot(x)^2+csc(x)-19	$\cot^{2} (x) + \csc (x) - 19$
40627	Factor	tan(x)^3-1	$\tan^{3} (x) - 1$
40628	Convert to Rectangular	theta=pi/3	$θ = \frac{π}{3}$
40629	Convert to Rectangular	theta=(5pi)/6	$θ = \frac{5 π}{6}$
40630	Find All Complex Solutions	cos(theta)^2-sin(theta)^2=1-sin(theta)	$\cos^{2} (θ) - \sin^{2} (θ) = 1 - \sin (θ)$
40631	Find the Roots (Zeros)	f(x)=x^4+290x^2+289	$f (x) = x^{4} + 290 x^{2} + 289$
40632	Find the Roots (Zeros)	f(x)=x^3-3x^2-49x+147	$f (x) = x^{3} - 3 x^{2} - 49 x + 147$
40633	Expand the Logarithmic Expression	log of square root of x^5yz^3	$\log (\sqrt{x^{5} y z^{3}})$
40634	Expand the Logarithmic Expression	log of (x^5)/( cube root of y^2z)	$\log (\frac{x^{5}}{\sqrt[3]{y^{2} z}})$
40635	Find the Roots (Zeros)	(x^3+8x^2-3x-90)÷(x+5)	$(x^{3} + 8 x^{2} - 3 x - 90) \div (x + 5)$
40636	Split Using Partial Fraction Decomposition	(x^2)/(x^2+16x+64)	$\frac{x^{2}}{x^{2} + 16 x + 64}$
40637	Expand the Trigonometric Expression	(1-x)^2	${(1 - x)}^{2}$
40638	Find Amplitude, Period, and Phase Shift	y=4cos(3x-pi)	$y = 4 \cos (3 x - π)$
40639	Find Amplitude, Period, and Phase Shift	y=3cos(4x+pi/2)	$y = 3 \cos (4 x + \frac{π}{2})$
40640	Find Amplitude, Period, and Phase Shift	y=-1/4sin(2x)	$y = - \frac{1}{4} \sin (2 x)$
40641	Find Amplitude, Period, and Phase Shift	y=-3cos(4x+pi/3)	$y = - 3 \cos (4 x + \frac{π}{3})$
40642	Verify the Identity	(tan(theta))/(sec(theta))=1/(cos(theta))-cos(theta)	$\frac{\tan (θ)}{\sec (θ)} = \frac{1}{\cos (θ)} - \cos (θ)$
40643	Verify the Identity	sec(theta)-cos(theta)=sin(theta)tan(theta)	$\sec (θ) - \cos (θ) = \sin (θ) \tan (θ)$
40644	Verify the Identity	cos(2u)=cos(u)^2-sin(u)^2	$\cos (2 u) = \cos^{2} (u) - \sin^{2} (u)$
40645	Convert to Interval Notation	(4x-9)^4(x-1)^3(x+1)<=0	${(4 x - 9)}^{4} {(x - 1)}^{3} (x + 1) \leq 0$
40646	Convert to Interval Notation	(-x+5)/(x-7)>=0	$\frac{- x + 5}{x - 7} \geq 0$
40647	Convert to Interval Notation	(x+4)(x-5)(x-8)<=0	$(x + 4) (x - 5) (x - 8) \leq 0$
40648	Find the Asymptotes	f(x)=-4tan(3pix)	$f (x) = - 4 \tan (3 π x)$
40649	Find the Asymptotes	f(x)=5tan(1/4x+pi/4)-2	$f (x) = 5 \tan (\frac{1}{4} x + \frac{π}{4}) - 2$
40650	Find the Asymptotes	f(x)=(x^3-9x)/(3x^2-6x-9)	$f (x) = \frac{x^{3} - 9 x}{3 x^{2} - 6 x - 9}$
40651	Find the Equation Given the Roots	3-7i	$3 - 7 i$
40652	Find the Roots/Zeros Using the Rational Roots Test	x^4-4x^3-3x^2+16x-4=0	$x^{4} - 4 x^{3} - 3 x^{2} + 16 x - 4 = 0$
40653	Find the Asymptotes	y=tan(x+pi/3)	$y = \tan (x + \frac{π}{3})$
40654	Multiply	(x-3)(x-2i)(x+2i)	$(x - 3) (x - 2 i) (x + 2 i)$
40655	Multiply	(sin(theta))/(1-cos(theta))*(1+cos(theta))/(1+cos(theta))	$\frac{\sin (θ)}{1 - \cos (θ)} \cdot \frac{1 + \cos (θ)}{1 + \cos (θ)}$
40656	Multiply	(cos(theta))/(sin(theta)-1)*(sin(theta)+1)/(sin(theta)+1)	$\frac{\cos (θ)}{\sin (θ) - 1} \cdot \frac{\sin (θ) + 1}{\sin (θ) + 1}$
40657	Multiply	(x-2)(x-2i)(x+2i)	$(x - 2) (x - 2 i) (x + 2 i)$
40658	Multiply	64*4	$64 \cdot 4$
40659	Divide	180/8	$\frac{180}{8}$
40660	Divide	(2pi)/(4pi)	$\frac{2 π}{4 π}$
40661	Divide	(2pi)/(4/3)	$\frac{2 π}{\frac{4}{3}}$
40662	Divide	1/(12/13)	$\frac{1}{\frac{12}{13}}$
40663	Find the Vertex	f(x)=2x^2-8x+10	$f (x) = 2 x^{2} - 8 x + 10$
40664	Find the Trig Value	tan(theta)=3/4	$\tan (θ) = \frac{3}{4}$
40665	Find the Trig Value	cos(theta)=-3/5	$\cos (θ) = - \frac{3}{5}$
40666	Convert to Rectangular Coordinates	(1,90 degrees )	$(1, 90 °)$
40667	Convert to Rectangular Coordinates	(pi,pi)	$(π, π)$
40668	Convert to Rectangular Coordinates	(-1,180 degrees )	$(- 1, 180 °)$
40669	Find the x and y Intercepts	f(x)=x^2-9x-22	$f (x) = x^{2} - 9 x - 22$
40670	Find dy/dx	x = square root of y+ fourth root of y	$x = \sqrt{y} + \sqrt[4]{y}$
40671	Find the Domain and Range	y=-2tan(x)	$y = - 2 \tan (x)$
40672	Find the Domain and Range	y=tan(pi/11x)	$y = \tan (\frac{π}{11} x)$
40673	Factor	x^3-15x^2+75x-125	$x^{3} - 15 x^{2} + 75 x - 125$
40674	Convert from Degrees to Radians	359 degrees	$359 °$
40675	Convert from Degrees to Radians	306 degrees	$306 °$
40676	Find the Degree	cot(theta)=1	$\cot (θ) = 1$
40677	Find the Inverse	y=arctan(x+pi/2)	$y = \tan^{-1} (x + \frac{π}{2})$
40678	Find the Center and Radius	(x+2)^2+(y-2)^2=25	${(x + 2)}^{2} + {(y - 2)}^{2} = 25$
40679	Simplify/Condense	tan(x)(cot(x)-csc(x))	$\tan (x (\cot (x) - \csc (x)))$
40680	Convert to Degrees, Minutes, and Seconds	270.58 degrees	$270.58 °$
40681	Expand Using Sum/Difference Formulas	sin(195 degrees )	$\sin (195 °)$
40682	Find All Complex Solutions	cos(theta)^2-sin(theta)^2=sin(theta)+1	$\cos^{2} (θ) - \sin^{2} (θ) = \sin (θ) + 1$
40683	Find All Complex Solutions	2sin(theta)^2-3sin(theta)+1=0	$2 \sin^{2} (θ) - 3 \sin (θ) + 1 = 0$
40684	Find All Complex Solutions	cos(x)=-( square root of 3)/2	$\cos (x) = - \frac{\sqrt{3}}{2}$
40685	Find All Complex Solutions	-sin(theta)^2+cos(theta)^2=sin(theta)+1	$- \sin^{2} (θ) + \cos^{2} (θ) = \sin (θ) + 1$
40686	Find the Asymptotes	(4-x^2)/(x^2-3x-4)	$\frac{4 - x^{2}}{x^{2} - 3 x - 4}$
40687	Convert to Logarithmic Form	6^(8x)=3.8	$6^{8 x} = 3.8$
40688	Find the Roots (Zeros)	12x^3-67x^2+36x-5=0	$12 x^{3} - 67 x^{2} + 36 x - 5 = 0$
40689	Find the x and y Intercepts	(x-8)/(x^2-64)	$\frac{x - 8}{x^{2} - 64}$
40690	Convert to Rectangular Coordinates	(-5,-180 degrees )	$(- 5, - 180 °)$
40691	Convert to Rectangular Coordinates	(1,0 degrees )	$(1, 0 °)$
40692	Write as a Single Logarithm	log base 2 of x+ log base 2 of x-3	$\log_{2} (x) + \log_{2} (x - 3)$
40693	Verify the Identity	(csc(theta)+1)(csc(theta)-1)=cot(theta)^2	$(\csc (θ) + 1) (\csc (θ) - 1) = \cot^{2} (θ)$
40694	Verify the Identity	cos(theta)*tan(theta)=sin(theta)	$\cos (θ) \cdot \tan (θ) = \sin (θ)$
40695	Verify the Identity	sec(theta)^2(1-sin(theta)^2)=1	$\sec^{2} (θ (1 - \sin^{2} (θ))) = 1$
40696	Verify the Identity	tan(theta)*cos(theta)=sin(theta)	$\tan (θ) \cdot \cos (θ) = \sin (θ)$
40697	Convert to Interval Notation	x^2+10x+25<=0	$x^{2} + 10 x + 25 \leq 0$
40698	Convert to Interval Notation	4x^4-25x^2+36<=0	$4 x^{4} - 25 x^{2} + 36 \leq 0$
40699	Convert to Interval Notation	(x-3)(x+6)<0	$(x - 3) (x + 6) < 0$
40700	Convert to Interval Notation	(3-x)^2(x-7/2)<0	${(3 - x)}^{2} (x - \frac{7}{2}) < 0$