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Trigonometry

Rank	Topic	Problem	Formatted Problem
51901	Find the Cosecant Given the Point	(1/5,-(2 square root of 6)/5)	$(\frac{1}{5}, - \frac{2 \sqrt{6}}{5})$
51902	Find the Cotangent Given the Point	(-1/5,(2 square root of 6)/5)	$(- \frac{1}{5}, \frac{2 \sqrt{6}}{5})$
51903	Find Amplitude, Period, and Phase Shift	y=2cos(4x+pi)-3	$y = 2 \cos (4 x + π) - 3$
51904	Solve for θ in Radians	square root of 3-tan(3theta)=0	$\sqrt{3} - \tan (3 θ) = 0$
51905	Convert to Rectangular Coordinates	(4 square root of 3,0)	$(4 \sqrt{3}, 0)$
51906	Solve for θ in Degrees	csc(theta)^2-9csc(theta)+20=0	$\csc^{2} (θ) - 9 \csc (θ) + 20 = 0$
51907	Find Amplitude, Period, and Phase Shift	y=cos((xpi)/3)	$y = \cos (\frac{x π}{3})$
51908	Find the Reference Angle	cos(-pi/4)	$\cos (- \frac{π}{4})$
51909	Convert from Degrees to Radians	200deg	$200$ degrees
51910	Find Amplitude, Period, and Phase Shift	y=-2tan(x-pi/4)+1	$y = - 2 \tan (x - \frac{π}{4}) + 1$
51911	Solve for θ in Radians	sin(2theta)+ square root of 3cos(theta)=0	$\sin (2 θ) + \sqrt{3} \cos (θ) = 0$
51912	Find Amplitude, Period, and Phase Shift	F(x)=3sin(2x-2)	$F (x) = 3 \sin (2 x - 2)$
51913	Convert from Degrees to Radians	480deg	$480$ degrees
51914	Convert from Radians to Degrees	sin(pi/4)	$\sin (\frac{π}{4})$
51915	Find Amplitude, Period, and Phase Shift	y=3csc(2x)+3/2	$y = 3 \csc (2 x) + \frac{3}{2}$
51916	Expand Using Sum/Difference Formulas	sin(pi+x)	$\sin (π + x)$
51917	Find the Reference Angle	cos(390 degrees )	$\cos (390 °)$
51918	Expand Using Sum/Difference Formulas	3(2x+1)+2(x+4)	$3 (2 x + 1) + 2 (x + 4)$
51919	Convert from Degrees to Radians	-45deg	$- 45$ degrees
51920	Find Trig Functions Using Identities	tan(theta)=24/7 , sin(theta)>0	$\tan (θ) = \frac{24}{7}$ , $\sin (θ) > 0$
51921	Solve for θ in Degrees	-2cos(theta)^2+sin(theta)+1=0	$- 2 \cos^{2} (θ) + \sin (θ) + 1 = 0$
51922	Find the Secant Given the Point	(( square root of 5)/5,-(2 square root of 5)/5)	$(\frac{\sqrt{5}}{5}, - \frac{2 \sqrt{5}}{5})$
51923	Find the Reference Angle	sin(765 degrees )	$\sin (765 °)$
51924	Verify the Identity	tan(-x)cot(x)=-1	$\tan (- x) \cot (x) = - 1$
51925	Expand Using Sum/Difference Formulas	sin(A+B)+sin(A-B)	$\sin (A + B) + \sin (A - B)$
51926	Expand Using Sum/Difference Formulas	tan(u+pi)	$\tan (u + π)$
51927	Solve for x in Degrees	5sin(x)tan(x)-4tan(x)=0	$5 \sin (x) \tan (x) - 4 \tan (x) = 0$
51928	Expand Using Sum/Difference Formulas	cos(a-B)+cos(a+B)	$\cos (a - B) + \cos (a + B)$
51929	Solve for θ in Degrees	2sin(theta)^2+3sin(theta)=0	$2 \sin^{2} (θ) + 3 \sin (θ) = 0$
51930	Find Amplitude, Period, and Phase Shift	y=3sin((pix)/3-(2pi)/3)	$y = 3 \sin (\frac{π x}{3} - \frac{2 π}{3})$
51931	Solve for x in Radians	sin(2x)-sin(x)=0	$\sin (2 x) - \sin (x) = 0$
51932	Solve for θ in Degrees	8tan(theta)-12=5tan(theta)-9	$8 \tan (θ) - 12 = 5 \tan (θ) - 9$
51933	Verify the Identity	(2x+2)/(x+1)=2	$\frac{2 x + 2}{x + 1} = 2$
51934	Solve for θ in Degrees	cot(theta)^2-6cot(theta)+8=0	$\cot^{2} (θ) - 6 \cot (θ) + 8 = 0$
51935	Solve for θ in Degrees	cos(theta)^2-cos(theta)=0	$\cos^{2} (θ) - \cos (θ) = 0$
51936	Find the Reference Angle	tan(300 degrees )	$\tan (300 °)$
51937	Convert from Radians to Degrees	arctan(( square root of 3)/2)	$\arctan (\frac{\sqrt{3}}{2})$
51938	Solve for x in Radians	cos(2x)-cos(x)=0	$\cos (2 x) - \cos (x) = 0$
51939	Convert from Degrees to Radians	390deg	$390$ degrees
51940	Convert from Radians to Degrees	0pi	$0 π$
51941	Verify the Identity	(sec(x)+1)/(tan(x))=(sin(x))/(1-cos(x))	$\frac{\sec (x) + 1}{\tan (x)} = \frac{\sin (x)}{1 - \cos (x)}$
51942	Find the Reference Angle	330deg	$330$ degrees
51943	Convert from Degrees to Radians	-30deg	$- 30$ degrees
51944	Find the Secant Given the Point	((2 square root of 13)/13,-(3 square root of 13)/13)	$(\frac{2 \sqrt{13}}{13}, - \frac{3 \sqrt{13}}{13})$
51945	Find Trig Functions Using Identities	sec(theta)=2 , sin(theta)<0	$\sec (θ) = 2$ , $\sin (θ) < 0$
51946	Solve for A in Degrees	12sin(A)+4=4sin(A)+4	$12 \sin (A) + 4 = 4 \sin (A) + 4$
51947	Solve for x in Radians	3sin(x)^2-sin(x)-1=0	$3 \sin^{2} (x) - \sin (x) - 1 = 0$
51948	Find the Reference Angle	tan(-pi/3)	$\tan (- \frac{π}{3})$
51949	Find Amplitude, Period, and Phase Shift	y=4/5cos((pix)/2)	$y = \frac{4}{5} \cos (\frac{π x}{2})$
51950	Solve for z in Radians	z=3(cos(pi/6)+isin(pi/6))	$z = 3 (\cos (\frac{π}{6}) + i \sin (\frac{π}{6}))$
51951	Find Amplitude, Period, and Phase Shift	f(x)=2-sin(x/4)	$f (x) = 2 - \sin (\frac{x}{4})$
51952	Find Amplitude, Period, and Phase Shift	y=4sin((2pix)/5-1)	$y = 4 \sin (\frac{2 π x}{5} - 1)$
51953	Solve for θ in Radians	2cos(theta)^2+cos(theta)=0	$2 \cos^{2} (θ) + \cos (θ) = 0$
51954	Convert from Radians to Degrees	cos(( square root of 2)/2)	$\cos (\frac{\sqrt{2}}{2})$
51955	Verify the Identity	(n root of a)^n=a	${(\sqrt[n]{a})}^{n} = a$
51956	Find Amplitude, Period, and Phase Shift	y=sin(3pix-(2pi)/3)	$y = \sin (3 π x - \frac{2 π}{3})$
51957	Find Amplitude, Period, and Phase Shift	y=sin((4x)/3+pi)	$y = \sin (\frac{4 x}{3} + π)$
51958	Expand Using Sum/Difference Formulas	x(x+2)	$x (x + 2)$
51959	Find the Sine Given the Point	((3 square root of 10)/10,-( square root of 10)/10)	$(\frac{3 \sqrt{10}}{10}, - \frac{\sqrt{10}}{10})$
51960	Convert from Degrees to Radians	-240deg	$- 240$ degrees
51961	Find the Value Using the Unit Circle	sec(90 degrees )	$\sec (90 °)$
51962	Find Amplitude, Period, and Phase Shift	y=sin((8pix)/3+pi/2)	$y = \sin (\frac{8 π x}{3} + \frac{π}{2})$
51963	Find Amplitude, Period, and Phase Shift	y=-1/2sec(x)	$y = - \frac{1}{2} \sec (x)$
51964	Solve for x in Radians	sin(x)^2=1/4	$\sin^{2} (x) = \frac{1}{4}$
51965	Find the Reference Angle	cot(-pi/6)	$\cot (- \frac{π}{6})$
51966	Find Amplitude, Period, and Phase Shift	y=2cos(3x-pi)+4 ?	$y = 2 \cos (3 x - π) + 4$ ?
51967	Solve for θ in Degrees	-4sin(theta)+5=3sin(theta)+5	$- 4 \sin (θ) + 5 = 3 \sin (θ) + 5$
51968	Convert from Radians to Degrees	sin(30)	$\sin (30)$
51969	Solve for θ in Radians	tan(theta)=-1/( square root of 3)	$\tan (θ) = - \frac{1}{\sqrt{3}}$
51970	Find Amplitude, Period, and Phase Shift	f(x)=2-sin(1/2x)	$f (x) = 2 - \sin (\frac{1}{2} x)$
51971	Solve for x in Radians	square root of 3cot(x)=1	$\sqrt{3} \cot (x) = 1$
51972	Find Amplitude, Period, and Phase Shift	y=1-3sin(2/3x)	$y = 1 - 3 \sin (\frac{2}{3} x)$
51973	Convert from Radians to Degrees	(11pi)/6rad	$\frac{11 π}{6}$ rad
51974	Find the Cosecant Given the Point	(( square root of 10)/10,-(3 square root of 10)/10)	$(\frac{\sqrt{10}}{10}, - \frac{3 \sqrt{10}}{10})$
51975	Verify the Identity	cos(x-pi/4)=( square root of 2)/2(cos(x)+sin(x))	$\cos (x - \frac{π}{4}) = \frac{\sqrt{2}}{2} (\cos (x) + \sin (x))$
51976	Find the Secant Given the Point	(-1, square root of 2)	$(- 1, \sqrt{2})$
51977	Find the Secant Given the Point	(3, square root of 3)	$(3, \sqrt{3})$
51978	Find the Secant Given the Point	(5 1/2,-2 square root of 15)	$(5 \frac{1}{2}, - 2 \sqrt{15})$
51979	Find Amplitude, Period, and Phase Shift	y=10cos((2pi)/3(x+1/4))	$y = 10 \cos (\frac{2 π}{3} (x + \frac{1}{4}))$
51980	Find Trig Functions Using Identities	sin(theta)=2/3 , tan(theta)<0	$\sin (θ) = \frac{2}{3}$ , $\tan (θ) < 0$
51981	Convert from Radians to Degrees	sin(pi/6)	$\sin (\frac{π}{6})$
51982	Find Amplitude, Period, and Phase Shift	y=-1/2sin((3x)/2)	$y = - \frac{1}{2} \sin (\frac{3 x}{2})$
51983	Find the Cosine Given the Point	((3 square root of 10)/10,-( square root of 10)/10)	$(\frac{3 \sqrt{10}}{10}, - \frac{\sqrt{10}}{10})$
51984	Convert to Trigonometric Form	(1+cos(2y))/(sin(2y))	$\frac{1 + \cos (2 y)}{\sin (2 y)}$
51985	Solve for x in Degrees	csc(x)=2	$\csc (x) = 2$
51986	Convert to Rectangular Coordinates	(6 square root of 2,pi/4)	$(6 \sqrt{2}, \frac{π}{4})$
51987	Find Amplitude, Period, and Phase Shift	y=cos(6pix+pi/2)	$y = \cos (6 π x + \frac{π}{2})$
51988	Convert from Degrees to Radians	-120deg	$- 120$ degrees
51989	Find the Missing Angle	tri{}{}{}{}{}{}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = \\ a = \end{matrix} & \begin{matrix} A = \\ B = \\ C = \end{matrix} \end{matrix}$
51990	Find the Reference Angle	225deg	$225$ degrees
51991	Expand Using Sum/Difference Formulas	cos(u+pi)	$\cos (u + π)$
51992	Solve for x in Radians	2sin(x)^2+3cos(x)-3=0	$2 \sin^{2} (x) + 3 \cos (x) - 3 = 0$
51993	Convert from Radians to Degrees	16rad	$16$ rad
51994	Find the Value Using the Unit Circle	45	$45$
51995	Find Amplitude, Period, and Phase Shift	y=-4sin(x+pi)+2	$y = - 4 \sin (x + π) + 2$
51996	Find the Reference Angle	sec((13pi)/3)	$\sec (\frac{13 π}{3})$
51997	Find Amplitude, Period, and Phase Shift	y=5sin(2/3x+2/9pi)	$y = 5 \sin (\frac{2}{3} x + \frac{2}{9} π)$
51998	Expand Using Sum/Difference Formulas	cos(pi/3+B)	$\cos (\frac{π}{3} + B)$
51999	Solve for x in Radians	sin(2x+1.5)=-0.3	$\sin (2 x + 1.5) = - 0.3$
52000	Solve for t in Radians	2sin(t)^2-cos(t)-1=0	$2 \sin^{2} (t) - \cos (t) - 1 = 0$