Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
2201	Expand Using Sum/Difference Formulas	(tan(40)+tan(20))/(1-tan(40)tan(20))	$\frac{\tan (40) + \tan (20)}{1 - \tan (40) \tan (20)}$
2202	Expand Using Sum/Difference Formulas	cos((7pi)/4+pi/6)	$\cos (\frac{7 π}{4} + \frac{π}{6})$
2203	Expand Using Sum/Difference Formulas	cos(45-60)	$\cos (45 - 60)$
2204	Find Amplitude, Period, and Phase Shift	y=1/2*sin(5x)	$y = \frac{1}{2} \cdot \sin (5 x)$
2205	Find Amplitude, Period, and Phase Shift	y=1/2*cos(8x)	$y = \frac{1}{2} \cdot \cos (8 x)$
2206	Find Amplitude, Period, and Phase Shift	y=1/4*sin(3x+pi)	$y = \frac{1}{4} \cdot \sin (3 x + π)$
2207	Find Amplitude, Period, and Phase Shift	y=-1/5*cos(1/5x)	$y = - \frac{1}{5} \cdot \cos (\frac{1}{5} x)$
2208	Find Amplitude, Period, and Phase Shift	y=1/5*sin(x)	$y = \frac{1}{5} \cdot \sin (x)$
2209	Find Amplitude, Period, and Phase Shift	y=2/3*cos(x/2-pi/4)	$y = \frac{2}{3} \cdot \cos (\frac{x}{2} - \frac{π}{4})$
2210	Find Amplitude, Period, and Phase Shift	y=5/3*sin(-(2pi)/3x)	$y = \frac{5}{3} \cdot \sin (- \frac{2 π}{3} x)$
2211	Find Amplitude, Period, and Phase Shift	y=arctan(x)	$y = \arctan (x)$
2212	Find Amplitude, Period, and Phase Shift	y=1-1/2*sin(3x-pi/4)	$y = 1 - \frac{1}{2} \cdot \sin (3 x - \frac{π}{4})$
2213	Find Amplitude, Period, and Phase Shift	f(x)=6sin(1/4*(pix)-pi)-3	$f (x) = 6 \sin (\frac{1}{4} \cdot (π x) - π) - 3$
2214	Find Amplitude, Period, and Phase Shift	f(x)=sin(x/3)	$f (x) = \sin (\frac{x}{3})$
2215	Find Amplitude, Period, and Phase Shift	y=2sin(2x-pi/3)	$y = 2 \sin (2 x - \frac{π}{3})$
2216	Find Amplitude, Period, and Phase Shift	y=2cos(x-3)	$y = 2 \cos (x - 3)$
2217	Find Amplitude, Period, and Phase Shift	y=2sec(1/2x-pi/3)	$y = 2 \sec (\frac{1}{2} x - \frac{π}{3})$
2218	Find Amplitude, Period, and Phase Shift	y=-2cos(x/4)	$y = - 2 \cos (\frac{x}{4})$
2219	Find Amplitude, Period, and Phase Shift	y=11tan(4x-2)	$y = 11 \tan (4 x - 2)$
2220	Find Amplitude, Period, and Phase Shift	y=-4cos(6x)	$y = - 4 \cos (6 x)$
2221	Find Amplitude, Period, and Phase Shift	y=-4cos(3-2x)	$y = - 4 \cos (3 - 2 x)$
2222	Find Amplitude, Period, and Phase Shift	y=4cos(x-pi/2)	$y = 4 \cos (x - \frac{π}{2})$
2223	Find Amplitude, Period, and Phase Shift	y=4cot(x)	$y = 4 \cot (x)$
2224	Find Amplitude, Period, and Phase Shift	y=4csc(x-pi/2)	$y = 4 \csc (x - \frac{π}{2})$
2225	Find Amplitude, Period, and Phase Shift	y=4cos(x/2)-5	$y = 4 \cos (\frac{x}{2}) - 5$
2226	Find Amplitude, Period, and Phase Shift	y=4cos(1/2x)	$y = 4 \cos (\frac{1}{2} x)$
2227	Find Amplitude, Period, and Phase Shift	y=3cos(x/2)	$y = 3 \cos (\frac{x}{2})$
2228	Find Amplitude, Period, and Phase Shift	y=-3cos(-2x+pi/2)	$y = - 3 \cos (- 2 x + \frac{π}{2})$
2229	Verify the Identity	(1-cos(A)^2)(1+cot(A)^2)=1	$(1 - \cos^{2} (A)) (1 + \cot^{2} (A)) = 1$
2230	Find the Complement	tan(60)	$\tan (60)$
2231	Find the Complement	sin(77)	$\sin (77)$
2232	Verify the Identity	(cot(x)^2)/(csc(x)-1)=(1+sin(x))/(sin(x))	$\frac{\cot^{2} (x)}{\csc (x) - 1} = \frac{1 + \sin (x)}{\sin (x)}$
2233	Verify the Identity	(cot(t)^2)/(csc(t))=(1-sin(t)^2)/(sin(t))	$\frac{\cot^{2} (t)}{\csc (t)} = \frac{1 - \sin^{2} (t)}{\sin (t)}$
2234	Verify the Identity	(csc(6x)-cot(6x))/(csc(6x)+cot(6x))=tan(3x)	$\frac{\csc (6 x) - \cot (6 x)}{\csc (6 x) + \cot (6 x)} = \tan (3 x)$
2235	Verify the Identity	(cos(x))/(1-sin(x))=(1+csc(x))/(csc(x))	$\frac{\cos (x)}{1 - \sin (x)} = \frac{1 + \csc (x)}{\csc (x)}$
2236	Verify the Identity	(cos(a+b))/(cos(a)sin(b))=cot(b)-tan(a)	$\frac{\cos (a + b)}{\cos (a) \sin (b)} = \cot (b) - \tan (a)$
2237	Verify the Identity	(1+sin(x))/(1-sin(x))=(sec(x)+tan(x))^2	$\frac{1 + \sin (x)}{1 - \sin (x)} = {(\sec (x) + \tan (x))}^{2}$
2238	Find the Supplement	(7pi)/6	$\frac{7 π}{6}$
2239	Find the Supplement	(9pi)/11	$\frac{9 π}{11}$
2240	Find the Supplement	240	$240$
2241	Find the Supplement	135	$135$
2242	Find the Reference Angle	20 degrees	$20 °$
2243	Find the Reference Angle	-404 degrees	$- 404 °$
2244	Find the Reference Angle	275 degrees	$275 °$
2245	Find the Reference Angle	345	$345$
2246	Find the Reference Angle	cos(150)	$\cos (150)$
2247	Find the Reference Angle	tan(150)	$\tan (150)$
2248	Verify the Identity	cot(x)=(1+cos(2x))/(sin(2x))	$\cot (x) = \frac{1 + \cos (2 x)}{\sin (2 x)}$
2249	Verify the Identity	sec(x)sin(x)cot(x)=1	$\sec (x) \cdot \sin (x) \cdot \cot (x) = 1$
2250	Verify the Identity	sec(-x)sin(x)=tan(x)	$\sec (- x) \sin (x) = \tan (x)$
2251	Verify the Identity	cos(pi/3+x)+cos(pi/3-x)=cos(x)	$\cos (\frac{π}{3} + x) + \cos (\frac{π}{3} - x) = \cos (x)$
2252	Verify the Identity	4csc(2x)=2csc(x)^2tan(x)	$4 \csc (2 x) = 2 \csc^{2} (x) \tan (x)$
2253	Verify the Identity	cot(y)^2(sec(y)^2-1)=1	$\cot^{2} (y) (\sec^{2} (y) - 1) = 1$
2254	Verify the Identity	1-cos(6x)=3sin(2x)	$1 - \cos (6 x) = 3 \sin (2 x)$
2255	Find the Exact Value	cos(-75)	$\cos (- 75)$
2256	Find the Exact Value	cos(960)	$\cos (960)$
2257	Find the Exact Value	cos(arctan(-2))	$\cos (\arctan (- 2))$
2258	Find the Exact Value	cos(arctan(11/60))	$\cos (\arctan (\frac{11}{60}))$
2259	Find the Exact Value	cos(arctan(3/4))	$\cos (\arctan (\frac{3}{4}))$
2260	Find the Exact Value	(cos(-7pi))/2	$\frac{\cos (- 7 π)}{2}$
2261	Find the Exact Value	cot(2/3*pi)	$\cot (\frac{2}{3} \cdot π)$
2262	Find the Exact Value	cos(-165)	$\cos (- 165)$
2263	Find the Exact Value	cos(157.5)	$\cos (157.5)$
2264	Find the Exact Value	cos(-315)	$\cos (- 315)$
2265	Find the Exact Value	cos(255)-cos(195)	$\cos (255) - \cos (195)$
2266	Find the Exact Value	cos(280)	$\cos (280)$
2267	Find the Exact Value	cos(112.5)	$\cos (112.5)$
2268	Find the Exact Value	cos(112)	$\cos (112)$
2269	Find the Exact Value	cos(pi/3+pi/4)	$\cos (\frac{π}{3} + \frac{π}{4})$
2270	Find the Exact Value	cos(-pi/9)	$\cos (- \frac{π}{9})$
2271	Find the Exact Value	cos(arctan(5/2))	$\cos (\arctan (\frac{5}{2}))$
2272	Find the Exact Value	cos(arcsin(7/8))	$\cos (\arcsin (\frac{7}{8}))$
2273	Find the Exact Value	cos(5/3*pi)	$\cos (\frac{5}{3} \cdot π)$
2274	Find the Exact Value	cos((4pi)/5)	$\cos (\frac{4 π}{5})$
2275	Find the Exact Value	cos(9/8*pi)	$\cos (\frac{9}{8} \cdot π)$
2276	Find the Exact Value	cos(arccos(-0.2))	$\cos (\arccos (- 0.2))$
2277	Find the Exact Value	cos((-19pi)/2)	$\cos (\frac{- 19 π}{2})$
2278	Find the Exact Value	cos(-1/3)	$\cos (- \frac{1}{3})$
2279	Find the Exact Value	arctan(tan(100))	$\arctan (\tan (100))$
2280	Find the Exact Value	arcsin(300)	$\arcsin (300)$
2281	Find the Exact Value	arcsin(sin(-(2pi)/3))	$\arcsin (\sin (- \frac{2 π}{3}))$
2282	Find the Exact Value	sec(-270)	$\sec (- 270)$
2283	Find the Exact Value	sec(-45)	$\sec (- 45)$
2284	Find the Exact Value	sec(1.24)	$\sec (1.24)$
2285	Find the Exact Value	sec(1.3)	$\sec (1.3)$
2286	Find the Exact Value	sec(14pi)	$\sec (14 π)$
2287	Find the Exact Value	sec(22)	$\sec (22)$
2288	Find the Exact Value	sec(20)	$\sec (20)$
2289	Find the Exact Value	sec(-20)	$\sec (- 20)$
2290	Find the Exact Value	sec((-7pi)/2)	$\sec (\frac{- 7 π}{2})$
2291	Find the Exact Value	sin((-16pi)/3)	$\sin (\frac{- 16 π}{3})$
2292	Find the Exact Value	sin((23pi)/12)	$\sin (\frac{23 π}{12})$
2293	Find the Exact Value	sec(arctan(-3/5))	$\sec (\arctan (\frac{- 3}{5}))$
2294	Find the Exact Value	sin((2pi)/3+(3pi)/4)	$\sin (\frac{2 π}{3} + \frac{3 π}{4})$
2295	Find the Exact Value	sin(3/8*pi)	$\sin (\frac{3}{8} \cdot π)$
2296	Find the Exact Value	sin((7pi)/6-pi/3)	$\sin (\frac{7 π}{6} - \frac{π}{3})$
2297	Find the Exact Value	sin(9/4*pi)	$\sin (\frac{9}{4} \cdot π)$
2298	Find the Exact Value	sec(13/3*pi)	$\sec (\frac{13}{3} \cdot π)$
2299	Find the Exact Value	csc(7/3*pi)	$\csc (\frac{7}{3} \cdot π)$
2300	Find the Exact Value	cot(arccos(-15/17))	$\cot (\arccos (- \frac{15}{17}))$