Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
2001	Verify the Identity	1/(1-sin(x))+1/(1+sin(x))=2sec(x)^2	$\frac{1}{1 - \sin (x)} + \frac{1}{1 + \sin (x)} = 2 \sec^{2} (x)$
2002	Verify the Identity	(1-sin(x))/(1+sin(x))=(sec(x)-tan(x))^2	$\frac{1 - \sin (x)}{1 + \sin (x)} = {(\sec (x) - \tan (x))}^{2}$
2003	Verify the Identity	cos(x)(tan(x)+cot(x))=csc(x)	$\cos (x) (\tan (x) + \cot (x)) = \csc (x)$
2004	Verify the Identity	2sin(x)+1=0	$2 \sin (x) + 1 = 0$
2005	Verify the Identity	cot(x-y)=(1+cot(y)cot(x))/(cot(y)-cot(x))	$\cot (x - y) = \frac{1 + \cot (y) \cot (x)}{\cot (y) - \cot (x)}$
2006	Verify the Identity	cot(x)sec(x)sin(x)=1	$\cot (x) \sec (x) \sin (x) = 1$
2007	Verify the Identity	cos(pi/2+x)=-sin(x)	$\cos (\frac{π}{2} + x) = - \sin (x)$
2008	Verify the Identity	cos(x)+sin(x)*tan(x)=sec(x)	$\cos (x) + \sin (x) \cdot \tan (x) = \sec (x)$
2009	Verify the Identity	sin(x)^4-cos(x)^4=2sin(x)^2-1	$\sin^{4} (x) - \cos^{4} (x) = 2 \sin^{2} (x) - 1$
2010	Verify the Identity	1-(cos(x)^2)/(1+sin(x))=sin(x)	$1 - \frac{\cos^{2} (x)}{1 + \sin (x)} = \sin (x)$
2011	Verify the Identity	1+sec(x)^2sin(x)^2=sec(x)^2	$1 + \sec^{2} (x) \sin^{2} (x) = \sec^{2} (x)$
2012	Verify the Identity	sin(pi/2+x)=cos(x)	$\sin (\frac{π}{2} + x) = \cos (x)$
2013	Verify the Identity	sin(2x)=2sin(x)cos(x)	$\sin (2 x) = 2 \sin (x) \cos (x)$
2014	Verify the Identity	sin(pi-x)=sin(x)	$\sin (π - x) = \sin (x)$
2015	Verify the Identity	sec(x)+tan(x)=(cos(x))/(1-sin(x))	$\sec (x) + \tan (x) = \frac{\cos (x)}{1 - \sin (x)}$
2016	Verify the Identity	sin(x+pi/2)=cos(x)	$\sin (x + \frac{π}{2}) = \cos (x)$
2017	Find the Exact Value	arcsin(30)	$\arcsin (30)$
2018	Find the Exact Value	cos((23pi)/4)	$\cos (\frac{23 π}{4})$
2019	Find the Exact Value	cos((29pi)/6)	$\cos (\frac{29 π}{6})$
2020	Find the Exact Value	cos(-3/5)	$\cos (- \frac{3}{5})$
2021	Find the Exact Value	cos(15/17)	$\cos (\frac{15}{17})$
2022	Find the Exact Value	cos(2/3)	$\cos (\frac{2}{3})$
2023	Find the Exact Value	cos(-(13pi)/4)	$\cos (- \frac{13 π}{4})$
2024	Find the Exact Value	cot(1)	$\cot (1)$
2025	Find the Exact Value	arccot(-6)	$arccot (- 6)$
2026	Find the Exact Value	cot(-45 degrees )	$\cot (- 45 °)$
2027	Find the Exact Value	cos(pi/4)^2	$\cos^{2} (\frac{π}{4})$
2028	Find the Exact Value	sec(-45 degrees )	$\sec (- 45 °)$
2029	Find the Exact Value	sec(90 degrees )	$\sec (90 °)$
2030	Find the Exact Value	sin((10pi)/3)	$\sin (\frac{10 π}{3})$
2031	Expand the Trigonometric Expression	sec(x)^2	$\sec^{2} (x)$
2032	Expand the Trigonometric Expression	cos(2x)	$\cos (2 x)$
2033	Expand the Trigonometric Expression	cos(pi/2-x)	$\cos (\frac{π}{2} - x)$
2034	Find the Value Using the Unit Circle	sin(30)	$\sin (30)$
2035	Find the Value Using the Unit Circle	cos((3pi)/8)	$\cos (\frac{3 π}{8})$
2036	Find the Value Using the Unit Circle	cos((4pi)/3)	$\cos (\frac{4 π}{3})$
2037	Find the Value Using the Unit Circle	arccos(-1/2)	$\arccos (- \frac{1}{2})$
2038	Expand the Trigonometric Expression	cot(x)	$\cot (x)$
2039	Find the Exact Value	sin(660)	$\sin (660)$
2040	Find the Exact Value	cot((27pi)/2)	$\cot (\frac{27 π}{2})$
2041	Find the Exact Value	cos(3pi)	$\cos (3 π)$
2042	Find the Exact Value	tan(-(5pi)/6)	$\tan (- \frac{5 π}{6})$
2043	Find the Exact Value	sin(78)	$\sin (78)$
2044	Find the Exact Value	csc(-240 degrees )	$\csc (- 240 °)$
2045	Find the Exact Value	tan(57/82)	$\tan (\frac{57}{82})$
2046	Find the Exact Value	tan(6/8)	$\tan (\frac{6}{8})$
2047	Find the Exact Value	tan(pi/10)	$\tan (\frac{π}{10})$
2048	Find the Exact Value	tan(pi/7)	$\tan (\frac{π}{7})$
2049	Find the Exact Value	tan(arcsin(-3/5))	$\tan (\arcsin (- \frac{3}{5}))$
2050	Find the Exact Value	tan(4/5)	$\tan (\frac{4}{5})$
2051	Find the Exact Value	tan((-3pi)/4)	$\tan (\frac{- 3 π}{4})$
2052	Find the Exact Value	tan((-11pi)/6)	$\tan (\frac{- 11 π}{6})$
2053	Find the Exact Value	tan(12/5)	$\tan (\frac{12}{5})$
2054	Find the Exact Value	sin(405)	$\sin (405)$
2055	Find the Exact Value	tan(21)	$\tan (21)$
2056	Find the Exact Value	tan(-225 degrees )	$\tan (- 225 °)$
2057	Find the Exact Value	tan(-3pi)	$\tan (- 3 π)$
2058	Find the Exact Value	tan(450)	$\tan (450)$
2059	Find the Exact Value	tan(arccos(3/4))	$\tan (\arccos (\frac{3}{4}))$
2060	Find the Exact Value	tan(15)	$\tan (15)$
2061	Find the Exact Value	sin((23pi)/6)	$\sin (\frac{23 π}{6})$
2062	Find the Exact Value	sin(-4/5)	$\sin (- \frac{4}{5})$
2063	Find the Exact Value	arcsec( square root of 2)	$arcsec (\sqrt{2})$
2064	Find the Exact Value	sin((7pi)/3)	$\sin (\frac{7 π}{3})$
2065	Find the Exact Value	sec(-30 degrees )	$\sec (- 30 °)$
2066	Find the Exact Value	csc(75)	$\csc (75)$
2067	Find the Exact Value	sin(5pi)	$\sin (5 π)$
2068	Find the Exact Value	sin(1/3)	$\sin (\frac{1}{3})$
2069	Find the Exact Value	csc(-120 degrees )	$\csc (- 120 °)$
2070	Find the Exact Value	sin((27pi)/2)	$\sin (\frac{27 π}{2})$
2071	Find the Exact Value	sec(7)	$\sec (7)$
2072	Find the Exact Value	tan(-330 degrees )	$\tan (- 330 °)$
2073	Find the Exact Value	sec(4pi)	$\sec (4 π)$
2074	Find the Exact Value	sec(3)	$\sec (3)$
2075	Find the Exact Value	sec(4)	$\sec (4)$
2076	Find the Exact Value	sec(390)	$\sec (390)$
2077	Find the Exact Value	csc((11pi)/4)	$\csc (\frac{11 π}{4})$
2078	Find the Exact Value	cos(-210 degrees )	$\cos (- 210 °)$
2079	Find the Exact Value	csc(-150 degrees )	$\csc (- 150 °)$
2080	Find the Exact Value	csc(360)	$\csc (360)$
2081	Find the Exact Value	cos((27pi)/2)	$\cos (\frac{27 π}{2})$
2082	Find the Exact Value	cos(arctan(1))	$\cos (\arctan (1))$
2083	Find the Exact Value	cot((2pi)/9)	$\cot (\frac{2 π}{9})$
2084	Find the Exact Value	cot((13pi)/6)	$\cot (\frac{13 π}{6})$
2085	Find the Exact Value	csc(-(7pi)/6)	$\csc (- \frac{7 π}{6})$
2086	Find the Exact Value	cot(10)	$\cot (10)$
2087	Find the Exact Value	cot(pi/12)	$\cot (\frac{π}{12})$
2088	Find the Exact Value	cot((7pi)/3)	$\cot (\frac{7 π}{3})$
2089	Find the Exact Value	cot(pi/8)	$\cot (\frac{π}{8})$
2090	Find the Exact Value	sin(75)	$\sin (75)$
2091	Find the Exact Value	arccot( square root of 3)	$arccot (\sqrt{3})$
2092	Find the Exact Value	cos(53)	$\cos (53)$
2093	Find the Exact Value	cos(67)	$\cos (67)$
2094	Find the Exact Value	cos(-225 degrees )	$\cos (- 225 °)$
2095	Find the Exact Value	arcsin(0.5)	$\arcsin (0.5)$
2096	Find the Exact Value	sin(-(5pi)/6)	$\sin (- \frac{5 π}{6})$
2097	Find the Exact Value	cos(23)	$\cos (23)$
2098	Find the Exact Value	cos(-330)	$\cos (- 330)$
2099	Find the Exact Value	cos(-(9pi)/4)	$\cos (- \frac{9 π}{4})$
2100	Find the Value Using the Unit Circle	cot(90)	$\cot (90)$