Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
14901	Verify the Identity	arcsin(3/5)+arcsin(5/13)=arcsin(56/65)	$\arcsin (\frac{3}{5}) + \arcsin (\frac{5}{13}) = \arcsin (\frac{56}{65})$
14902	Verify the Identity	cos(x+pi/4)=( square root of 2)/2*(cos(x)-sin(x))	$\cos (x + \frac{π}{4}) = \frac{\sqrt{2}}{2} \cdot (\cos (x) - \sin (x))$
14903	Verify the Identity	cos(x-90)-cos(x+90)=2sin(x)	$\cos (x - 90) - \cos (x + 90) = 2 \sin (x)$
14904	Verify the Identity	cos(x)cos(3x)-sin(x)sin(3x)=0	$\cos (x) \cos (3 x) - \sin (x) \sin (3 x) = 0$
14905	Solve for x	x^3+729=0	$x^{3} + 729 = 0$
14906	Verify the Identity	cos(x)tan(x+1)^2=sec(x)	$\cos (x) \tan^{2} (x + 1) = \sec (x)$
14907	Verify the Identity	cos(x)(1+tan(x)^2)=sec(x)	$\cos (x) (1 + \tan^{2} (x)) = \sec (x)$
14908	Verify the Identity	cos(a-b)-cos(a+b)=2sin(a)sin(b)	$\cos (a - b) - \cos (a + b) = 2 \sin (a) \sin (b)$
14909	Verify the Identity	cos(8x)sin(16x)=(1-2sin(4x)^2)^2(2sin(8x))	$\cos (8 x) \sin (16 x) = {(1 - 2 \sin^{2} (4 x))}^{2} (2 \sin (8 x))$
14910	Verify the Identity	cos(pi/2-u)=sin(u)	$\cos (\frac{π}{2} - u) = \sin (u)$
14911	Verify the Identity	cos(3x)=cos(x)^3-3sin(x)^2cos(x)	$\cos (3 x) = \cos^{3} (x) - 3 \sin^{2} (x) \cos (x)$
14912	Verify the Identity	cos(4u)=cos(2u)^2-sin(2u)^2	$\cos (4 u) = \cos^{2} (2 u) - \sin^{2} (2 u)$
14913	Simplify	(1-i)^10	${(1 - i)}^{10}$
14914	Verify the Identity	cos(4x)+(cos(2x))÷(sin(4x))+sin(2x)=cot(3x)	$\cos (4 x) + \cos (2 x) \div \sin (4 x) + \sin (2 x) = \cot (3 x)$
14915	Verify the Identity	4sin(x)^2+7cos(x)^2=7-3sin(x)^2	$4 \sin^{2} (x) + 7 \cos^{2} (x) = 7 - 3 \sin^{2} (x)$
14916	Verify the Identity	3cos(x)+3=2sin(x)^2	$3 \cos (x) + 3 = 2 \sin^{2} (x)$
14917	Verify the Identity	-8tan(x)^2=2tan(x)-1	$- 8 \tan^{2} (x) = 2 \tan (x) - 1$
14918	Verify the Identity	5cos(2x)=-15cos(x)-10	$5 \cos (2 x) = - 15 \cos (x) - 10$
14919	Verify the Identity	5sin(x)-8 square root of 2=3sin(x)-7 square root of 2	$5 \sin (x) - 8 \sqrt{2} = 3 \sin (x) - 7 \sqrt{2}$
14920	Verify the Identity	6sin(x)cos(x)=3sin(2x)	$6 \sin (x) \cos (x) = 3 \sin (2 x)$
14921	Verify the Identity	cos(270-x)=-sin(x)	$\cos (270 - x) = - \sin (x)$
14922	Verify the Identity	cos(2x)+cos(4x)=0	$\cos (2 x) + \cos (4 x) = 0$
14923	Verify the Identity	2sec(x)^2=1/(1+sin(x))+1/(1-sin(x))	$2 \sec^{2} (x) = \frac{1}{1 + \sin (x)} + \frac{1}{1 - \sin (x)}$
14924	Verify the Identity	cos(x)=4/5	$\cos (x) = \frac{4}{5}$
14925	Verify the Identity	sin(2a)=2sin(a)	$\sin (2 a) = 2 \sin (a)$
14926	Verify the Identity	sin(3x)=3cos(x)^2sin(x)-sin(x)^3	$\sin (3 x) = 3 \cos^{2} (x) \sin (x) - \sin^{3} (x)$
14927	Verify the Identity	sin(2x)=tan(x)	$\sin (2 x) = \tan (x)$
14928	Verify the Identity	sin(3u)=3cos(u)^2sin(u)-sin(u)^3	$\sin (3 u) = 3 \cos^{2} (u) \sin (u) - \sin^{3} (u)$
14929	Verify the Identity	sin(3x)cos(x)-cos(3x)sin(x)=0	$\sin (3 x) \cos (x) - \cos (3 x) \sin (x) = 0$
14930	Verify the Identity	sin(20)-sin(40)-sin(60)=-4cos(x)sin(20)cos(30)	$\sin (20) - \sin (40) - \sin (60) = - 4 \cos (x) \sin (20) \cos (30)$
14931	Verify the Identity	sin(x/7)sin(x/7)=1/2*(1-cos((2x)/7))	$\sin (\frac{x}{7}) \sin (\frac{x}{7}) = \frac{1}{2} \cdot (1 - \cos (\frac{2 x}{7}))$
14932	Verify the Identity	sin(x)=15/17	$\sin (x) = \frac{15}{17}$
14933	Verify the Identity	sin(x)=20/29=cos(2x)	$\sin (x) = \frac{20}{29} = \cos (2 x)$
14934	Verify the Identity	sin(x)=381/914	$\sin (x) = \frac{381}{914}$
14935	Verify the Identity	sec(x-pi/2)=csc(x)	$\sec (x - \frac{π}{2}) = \csc (x)$
14936	Verify the Identity	sin(x)+cos(x)=(sin(x))/(1-cot(x))+(cos(x))/(1-tan(x))	$\sin (x) + \cos (x) = \frac{\sin (x)}{1 - \cot (x)} + \frac{\cos (x)}{1 - \tan (x)}$
14937	Verify the Identity	sec(x)=sec(x)sin(x)^2+cos(x)	$\sec (x) = \sec (x) \sin^{2} (x) + \cos (x)$
14938	Verify the Identity	sec(a+B)=(sec(a)sec(B))/(1-tan(a)tan(B))	$\sec (a + B) = \frac{\sec (a) \sec (B)}{1 - \tan (a) \tan (B)}$
14939	Verify the Identity	cot(x+y)=(cot(x)cot(y)-1)/(cot(y)-cot(x))	$\cot (x + y) = \frac{\cot (x) \cot (y) - 1}{\cot (y) - \cot (x)}$
14940	Verify the Identity	csc(2x)=1/2*(sec(x)csc(x))	$\csc (2 x) = \frac{1}{2} \cdot (\sec (x) \csc (x))$
14941	Verify the Identity	csc(x)(csc(x)-sin(x))+(sin(x)-cos(x))/(sin(x))+cot(x)=csc(x)^2	$\csc (x) (\csc (x) - \sin (x)) + \frac{\sin (x) - \cos (x)}{\sin (x)} + \cot (x) = \csc^{2} (x)$
14942	Verify the Identity	cos(X+(5pi)/2)=-sin(X)	$\cos (X + \frac{5 π}{2}) = - \sin (X)$
14943	Verify the Identity	csc(x)cos(x)tan(x)=1	$\csc (x) \cdot \cos (x) \cdot \tan (x) = 1$
14944	Verify the Identity	csc(x)sec(x)cot(x)=csc(x)^2	$\csc (x) \sec (x) \cot (x) = \csc^{2} (x)$
14945	Verify the Identity	r=2cos(x)	$r = 2 \cos (x)$
14946	Find the Reference Angle	tan(154)	$\tan (154)$
14947	Find the Reference Angle	tan(165)	$\tan (165)$
14948	Find the Reference Angle	tan(60)	$\tan (60)$
14949	Find the Reference Angle	cos(285)	$\cos (285)$
14950	Find the Reference Angle	csc(210)	$\csc (210)$
14951	Find the Reference Angle	sec(225)	$\sec (225)$
14952	Find the Reference Angle	csc(53)	$\csc (53)$
14953	Find the Reference Angle	cos(-45)	$\cos (- 45)$
14954	Find the Reference Angle	cos(270)	$\cos (270)$
14955	Find the Reference Angle	cot(120)	$\cot (120)$
14956	Find the Reference Angle	-830 degrees	$- 830 °$
14957	Find the Reference Angle	810	$810$
14958	Find the Reference Angle	-945 degrees	$- 945 °$
14959	Find the Reference Angle	8440 degrees	$8440 °$
14960	Find the Reference Angle	-750	$- 750$
14961	Find the Reference Angle	765	$765$
14962	Find the Reference Angle	665	$665$
14963	Find the Reference Angle	64 degrees	$64 °$
14964	Find the Reference Angle	-65	$- 65$
14965	Find the Reference Angle	560	$560$
14966	Find the Reference Angle	327 degrees	$327 °$
14967	Find the Reference Angle	-359	$- 359$
14968	Find the Reference Angle	275	$275$
14969	Evaluate the Limit	limit as n approaches infinity of (4n^3+7n^2)/(5n^3-7n^2+3)	$lim_{n \to \infty} \frac{4 n^{3} + 7 n^{2}}{5 n^{3} - 7 n^{2} + 3}$
14970	Find the Reference Angle	3.5	$3.5$
14971	Find the Reference Angle	245	$245$
14972	Find the Reference Angle	-265 degrees	$- 265 °$
14973	Find the Reference Angle	-27	$- 27$
14974	Find the Reference Angle	345 degrees	$345 °$
14975	Find the Reference Angle	371	$371$
14976	Find the Reference Angle	389	$389$
14977	Find the Reference Angle	-4	$- 4$
14978	Find the Reference Angle	37 degrees	$37 °$
14979	Find the Reference Angle	553	$553$
14980	Find the Reference Angle	-555	$- 555$
14981	Find the Reference Angle	570	$570$
14982	Find the Reference Angle	495	$495$
14983	Find the Reference Angle	-465 degrees	$- 465 °$
14984	Find the Complement	163 degrees	$163 °$
14985	Find the Complement	-170 degrees	$- 170 °$
14986	Find the Complement	33	$33$
14987	Find the Complement	1.41	$1.41$
14988	Find the Complement	120	$120$
14989	Find the Complement	-120 degrees	$- 120 °$
14990	Find the Complement	130	$130$
14991	Find the Complement	(4pi)/15	$\frac{4 π}{15}$
14992	Find the Complement	(5pi)/8	$\frac{5 π}{8}$
14993	Find the Complement	(9pi)/5	$\frac{9 π}{5}$
14994	Find the Supplement	sin(45)	$\sin (45)$
14995	Find the Supplement	cos(45)	$\cos (45)$
14996	Find the Supplement	cos(165)	$\cos (165)$
14997	Find the Supplement	sin(-1485)	$\sin (- 1485)$
14998	Find the Supplement	240 degrees	$240 °$
14999	Find the Supplement	16	$16$
15000	Find the Supplement	230	$230$