Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
45601	Convert to Trigonometric Form	-5+2i	$- 5 + 2 i$
45602	Convert to Trigonometric Form	6+3i	$6 + 3 i$
45603	Convert to Trigonometric Form	4+4i square root of 3	$4 + 4 i \sqrt{3}$
45604	Convert to Trigonometric Form	5	$5$
45605	Convert to Trigonometric Form	5(cos(25 degrees )+isin(25 degrees ))*2(cos(80 degrees )+isin(80 degrees ))	$5 (\cos (25 °) + i \sin (25 °)) \cdot 2 (\cos (80 °) + i \sin (80 °))$
45606	Convert to Trigonometric Form	5(cos(15 degrees )+isin(15 degrees ))*3(cos(70 degrees )+isin(70 degrees ))	$5 (\cos (15 °) + i \sin (15 °)) \cdot 3 (\cos (70 °) + i \sin (70 °))$
45607	Convert to Trigonometric Form	3-3 square root of 3i	$3 - 3 \sqrt{3 i}$
45608	Convert to Trigonometric Form	3-6i	$3 - 6 i$
45609	Convert to Trigonometric Form	-3-7i	$- 3 - 7 i$
45610	Convert to Trigonometric Form	-4 square root of 2(1-i)	$- 4 \sqrt{2} (1 - i)$
45611	Convert to Trigonometric Form	3- square root of 3i	$3 - \sqrt{3} i$
45612	Convert to Trigonometric Form	-1+5i	$- 1 + 5 i$
45613	Convert to Trigonometric Form	-14+14i	$- 14 + 14 i$
45614	Convert to Trigonometric Form	125i	$125 i$
45615	Convert to Trigonometric Form	12i	$12 i$
45616	Convert to Trigonometric Form	(5+5i)(8(cos((3pi)/7)+isin((3pi)/7)))	$(5 + 5 i) (8 (\cos (\frac{3 π}{7}) + i \sin (\frac{3 π}{7})))$
45617	Convert to Trigonometric Form	(6(cos(5pi)+isin(5pi)))/(3(cos(2pi)+isin(2pi)))	$\frac{6 (\cos (5 π) + i \sin (5 π))}{3 (\cos (2 π) + i \sin (2 π))}$
45618	Convert to Trigonometric Form	(2pi)/3	$\frac{2 π}{3}$
45619	Convert to Trigonometric Form	(-2-2i)^4	${(- 2 - 2 i)}^{4}$
45620	Convert to Trigonometric Form	(3cispi/6)^3	${(3 c i s \frac{π}{6})}^{3}$
45621	Convert to Trigonometric Form	cube root of -2i	$\sqrt[3]{- 2 i}$
45622	Convert to Trigonometric Form	sin(50 degrees )cos(170 degrees )-cos(50 degrees )sin(170 degrees )	$\sin (50 °) \cos (170 °) - \cos (50 °) \sin (170 °)$
45623	Convert to Trigonometric Form	square root of 2- square root of 2i	$\sqrt{2} - \sqrt{2} i$
45624	Convert to Trigonometric Form	(3/5(cos(pi/3)+isin(pi/3)))(5(cos((3pi)/5)+isin((3pi)/5)))	$(\frac{3}{5} (\cos (\frac{π}{3}) + i \sin (\frac{π}{3}))) (5 (\cos (\frac{3 π}{5}) + i \sin (\frac{3 π}{5})))$
45625	Convert to Trigonometric Form	(3(cos(27 degrees )+isin(27 degrees )))^5	${(3 (\cos (27 °) + i \sin (27 °)))}^{5}$
45626	Convert to Trigonometric Form	cos(45 degrees )	$\cos (45 °)$
45627	Convert to Trigonometric Form	-25i	$- 25 i$
45628	Convert to Trigonometric Form	-2+9i	$- 2 + 9 i$
45629	Convert to Trigonometric Form	20 square root of 3-20i	$20 \sqrt{3} - 20 i$
45630	Convert to Trigonometric Form	2 square root of 2-2i square root of 2	$2 \sqrt{2} - 2 i \sqrt{2}$
45631	Convert to Trigonometric Form	2cos(22.5 degrees )^2-1	$2 \cos^{2} (22.5 °) - 1$
45632	Verify the Identity	cos(theta)^2-sin(theta)^2=1+sin(theta)	$\cos^{2} (θ) - \sin^{2} (θ) = 1 + \sin (θ)$
45633	Verify the Identity	cos(theta)^4+1-sin(theta)^4=2cos(theta)^3	$\cos^{4} (θ) + 1 - \sin^{4} (θ) = 2 \cos^{3} (θ)$
45634	Verify the Identity	cos(2a)=cos(a)^2-sin(a)^2	$\cos (2 a) = \cos^{2} (a) - \sin^{2} (a)$
45635	Verify the Identity	tan(2pi+theta)=tan(theta)	$\tan (2 π + θ) = \tan (θ)$
45636	Verify the Identity	sin(B)sec(B)cot(B)=1	$\sin (B) \sec (B) \cot (B) = 1$
45637	Convert to Trigonometric Form	( square root of 2-i)^6	${(\sqrt{2} - i)}^{6}$
45638	Convert to Trigonometric Form	( square root of 3(cos((7pi)/6)+isin((7pi)/6)))^4	${(\sqrt{3} (\cos (\frac{7 π}{6}) + i \sin (\frac{7 π}{6})))}^{4}$
45639	Convert to Trigonometric Form	( square root of 3+i)^5	${(\sqrt{3} + i)}^{5}$
45640	Convert to Trigonometric Form	pi/2	$\frac{π}{2}$
45641	Factor over the Complex Numbers	3-14i	$3 - 14 i$
45642	Factor over the Complex Numbers	4-7i	$4 - 7 i$
45643	Convert to Trigonometric Form	6-4i	$6 - 4 i$
45644	Convert to Trigonometric Form	-81i	$- 81 i$
45645	Convert to Trigonometric Form	8 square root of 3-8i	$8 \sqrt{3} - 8 i$
45646	Convert to Trigonometric Form	8+5i	$8 + 5 i$
45647	Find the Cosine Given the Point	(3/7,-(2 square root of 10)/7)	$(\frac{3}{7}, - \frac{2 \sqrt{10}}{7})$
45648	Find the Cosine Given the Point	((3pi)/2,(7pi)/4)	$(\frac{3 π}{2}, \frac{7 π}{4})$
45649	Factor over the Complex Numbers	tan(arcsin(w))	$\tan (\arcsin (w))$
45650	Find the Cosine Given the Point	(5 1/2,-2 square root of 15)	$(5 \frac{1}{2}, - 2 \sqrt{15})$
45651	Convert to Interval Notation	5x^2+17x<12	$5 x^{2} + 17 x < 12$
45652	Convert to Interval Notation	6x^2-15x-4<8x	$6 x^{2} - 15 x - 4 < 8 x$
45653	Convert to Interval Notation	6x^3+25x^2-24x+5>0	$6 x^{3} + 25 x^{2} - 24 x + 5 > 0$
45654	Convert to Interval Notation	-7x<x+7	$- 7 x < x + 7$
45655	Convert to Interval Notation	-8<=3x+6<=1/2	$- 8 \leq 3 x + 6 \leq \frac{1}{2}$
45656	Convert to Interval Notation	3x<=20-2x^2	$3 x \leq 20 - 2 x^{2}$
45657	Convert to Interval Notation	3(x-1)(x+2)(x-3)>=0	$3 (x - 1) (x + 2) (x - 3) \geq 0$
45658	Convert to Interval Notation	x(x+6)^2(x-2)<=0	$x {(x + 6)}^{2} (x - 2) \leq 0$
45659	Convert to Interval Notation	x^2+2x>15	$x^{2} + 2 x > 15$
45660	Convert to Interval Notation	-10<=-3x+3<-5	$- 10 \leq - 3 x + 3 < - 5$
45661	Convert to Interval Notation	\|5x-3\|<=7	$\| 5 x - 3 \| \leq 7$
45662	Convert to Interval Notation	x^3-5x^2<=-4x+20	$x^{3} - 5 x^{2} \leq - 4 x + 20$
45663	Convert to Interval Notation	x^3-7x^2-18x>0	$x^{3} - 7 x^{2} - 18 x > 0$
45664	Convert to Interval Notation	x^3-2x^2>=0	$x^{3} - 2 x^{2} \geq 0$
45665	Convert to Interval Notation	x^3+9x^2<-6x+56	$x^{3} + 9 x^{2} < - 6 x + 56$
45666	Convert to Interval Notation	x^4>4x^2	$x^{4} > 4 x^{2}$
45667	Convert to Interval Notation	x^2>=3x+18	$x^{2} \geq 3 x + 18$
45668	Convert to Interval Notation	x^2>36	$x^{2} > 36$
45669	Convert to Interval Notation	x^2-4x+7<=0	$x^{2} - 4 x + 7 \leq 0$
45670	Solve the System of @WORD	2x^3+x^2+6>=13x	$2 x^{3} + x^{2} + 6 \geq 13 x$
45671	Solve the System of @WORD	4x+3y<=-62x-y<=-8	$4 x + 3 y \leq - 62 x - y \leq - 8$
45672	Convert to Interval Notation	x-3>0	$x - 3 > 0$
45673	Solve the System of @WORD	x^(3/5)>=15	$x^{\frac{3}{5}} \geq 15$
45674	Solve the System of @WORD	x^2+y^2+14x-12y+69=0x^2+6y^2+14x-72y+169=0	$x^{2} + y^{2} + 14 x - 12 y + 69 = 0 x^{2} + 6 y^{2} + 14 x - 72 y + 169 = 0$
45675	Solve the System of @WORD	x^2<4	$x^{2} < 4$
45676	Solve the System of @WORD	x^2-5x<=0	$x^{2} - 5 x \leq 0$
45677	Find the Inverse	[[2,2],[3,-7]]	$[\begin{array}{c} 2 & 2 \\ 3 & - 7 \end{array}]$
45678	Find the Inverse	[[2,1],[-4,3]]	$[\begin{array}{c} 2 & 1 \\ - 4 & 3 \end{array}]$
45679	Find the Inverse	[[13,3],[15,1]]	$[\begin{array}{c} 13 & 3 \\ 15 & 1 \end{array}]$
45680	Find the Inverse	[[-12,10],[6,-5]]	$[\begin{array}{c} - 12 & 10 \\ 6 & - 5 \end{array}]$
45681	Find the Inverse	[[-7,5],[12,2]]	$[\begin{array}{c} - 7 & 5 \\ 12 & 2 \end{array}]$
45682	Verify the Identity	(1-cos(x)^2)sec(x)=sin(x)^2sec(x)	$(1 - \cos^{2} (x)) \sec (x) = \sin^{2} (x) \sec (x)$
45683	Verify the Identity	(cos(x)-tan(x))/(sin(x)+cos(x))=csc(x)-sec(x)	$\frac{\cos (x) - \tan (x)}{\sin (x) + \cos (x)} = \csc (x) - \sec (x)$
45684	Verify the Identity	(cos(x)^3)/(sin(x))=cot(x)	$\frac{\cos^{3} (x)}{\sin (x)} = \cot (x)$
45685	Verify the Identity	(1-cos(theta)^2)(1+cot(theta)^2)=1	$(1 - \cos^{2} (θ)) (1 + \cot^{2} (θ)) = 1$
45686	Verify the Identity	(sin(A+B))/(sin(A-B))=(tan(A)+tan(B))/(tan(A)-tan(B))	$\frac{\sin (A + B)}{\sin (A - B)} = \frac{(\tan (A) + \tan (B))}{\tan (A) - \tan (B)}$
45687	Verify the Identity	(sec(theta)+tan(theta))/(sec(theta)-tan(theta))=(1+2sin(theta)+sin(theta)^2)/(cos(theta)^2)	$\frac{\sec (θ) + \tan (θ)}{\sec (θ) - \tan (θ)} = \frac{1 + 2 \sin (θ) + \sin^{2} (θ)}{\cos^{2} (θ)}$
45688	Verify the Identity	cos((3pi)/2+theta)=sin(theta)	$\cos (\frac{3 π}{2} + θ) = \sin (θ)$
45689	Verify the Identity	cos(pi-theta)=-cos(theta)	$\cos (π - θ) = - \cos (θ)$
45690	Verify the Identity	sin(theta)^2csc(theta)^2=sin(theta)^2+cos(theta)^2	$\sin^{2} (θ) \csc^{2} (θ) = \sin^{2} (θ) + \cos^{2} (θ)$
45691	Verify the Identity	sin(x+pi/6)-cos(x+pi/3) = square root of 3sin(x)	$\sin (x + \frac{π}{6}) - \cos (x + \frac{π}{3}) = \sqrt{3} \sin (x)$
45692	Verify the Identity	sin(theta)tan(theta)=sec(theta)-cos(theta)	$\sin (θ) \tan (θ) = \sec (θ) - \cos (θ)$
45693	Verify the Identity	sec(x)^2(1-sin(x)^2)=1	$\sec^{2} (x (1 - \sin^{2} (x))) = 1$
45694	Verify the Identity	sec(u)-tan(u)=(cos(u))/(1+sin(u))	$\sec (u) - \tan (u) = \frac{\cos (u)}{1 + \sin (u)}$
45695	Verify the Identity	arccsc(x)=1/(sin(x))	$arccsc (x) = \frac{1}{\sin (x)}$
45696	Verify the Identity	1+sec(theta)^2*sin(theta)^2=sec(theta)^2	$1 + \sec^{2} (θ) \cdot \sin^{2} (θ) = \sec^{2} (θ)$
45697	Find the Difference Quotient	f(x)=4x^2+7x	$f (x) = 4 x^{2} + 7 x$
45698	Find the Difference Quotient	f(x)=4x+4	$f (x) = 4 x + 4$
45699	Find the Difference Quotient	f(x)=4x^2+3x	$f (x) = 4 x^{2} + 3 x$
45700	Find the Difference Quotient	f(x)=-2x+4	$f (x) = - 2 x + 4$