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Trigonometry

Rank	Topic	Problem	Formatted Problem
52401	Find the Cotangent Given the Point	(-2 square root of 3,2)	$(- 2 \sqrt{3}, 2)$
52402	Find Amplitude, Period, and Phase Shift	y=cos(-2x+pi)-1	$y = \cos (- 2 x + π) - 1$
52403	Convert from Radians to Degrees	2*180/pi	$2 \cdot \frac{180}{π}$
52404	Convert from Radians to Degrees	sin(( square root of 3)/2)	$\sin (\frac{\sqrt{3}}{2})$
52405	Verify the Identity	x^3+y^3=(x+y)(x^2-xy+y^2)	$x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})$
52406	Convert from Degrees to Radians	arccot(cot((5pi)/4))	$arccot (\cot (\frac{5 π}{4}))$
52407	Find the Cotangent Given the Point	( square root of 2, square root of 2)	$(\sqrt{2}, \sqrt{2})$
52408	Find Amplitude, Period, and Phase Shift	y=sin(3x+2pi)	$y = \sin (3 x + 2 π)$
52409	Find the Cosine of the Angle	135 degrees	$135 °$
52410	Find Amplitude, Period, and Phase Shift	y=8/9cos((pix)/2)	$y = \frac{8}{9} \cos (\frac{π x}{2})$
52411	Convert from Radians to Degrees	-12pirad	$- 12 π$ radians
52412	Find the Coterminal Angle	13/2pi	$\frac{13}{2} π$
52413	Find Amplitude, Period, and Phase Shift	f(x)=2sin(2x)-pi/2	$f (x) = 2 \sin (2 x) - \frac{π}{2}$
52414	Solve for θ in Degrees	3tan(theta)+1=0	$3 \tan (θ) + 1 = 0$
52415	Verify the Identity	sin(A+B)=cos(pi/2-(A+B))	$\sin (A + B) = \cos (\frac{π}{2} - (A + B))$
52416	Find Amplitude, Period, and Phase Shift	y=1/4sin(x-(2pi)/3)	$y = \frac{1}{4} \sin (x - \frac{2 π}{3})$
52417	Verify the Identity	(csc(-x))/(sec(-x))=-cot(x)	$\frac{\csc (- x)}{\sec (- x)} = - \cot (x)$
52418	Solve for x in Degrees	3tan(x)sin(x)+2sin(x)=0	$3 \tan (x) \sin (x) + 2 \sin (x) = 0$
52419	Find the Sine of the Angle	(5pi)/4	$\frac{5 π}{4}$
52420	Convert from Radians to Degrees	-6pirad	$- 6 π$ radians
52421	Find the Length of b	tri{}{30}{4}{60}{}{90}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = & 4 \\ a = \end{matrix} & \begin{matrix} A = & 30 \\ B = & 60 \\ C = & 90 \end{matrix} \end{matrix}$
52422	Solve for x in Radians	2sin(x)^2=1	$2 \sin^{2} (x) = 1$
52423	Solve for x in Degrees	5tan(x)sin(x)-4sin(x)=0	$5 \tan (x) \sin (x) - 4 \sin (x) = 0$
52424	Convert from Radians to Degrees	(10pi)/9rad	$\frac{10 π}{9}$ radians
52425	Find the Sine of the Angle	60	$60$
52426	Find Amplitude, Period, and Phase Shift	y=4cos((6pix)/7-1/2)	$y = 4 \cos (\frac{6 π x}{7} - \frac{1}{2})$
52427	Expand the Trigonometric Expression	cot(-x)cos(-x)+sin(-x)	$\cot (- x) \cos (- x) + \sin (- x)$
52428	Solve for B in Degrees	5tan(B)+7=2tan(B)+4	$5 \tan (B) + 7 = 2 \tan (B) + 4$
52429	Expand Using Sum/Difference Formulas	3(x+2)	$3 (x + 2)$
52430	Solve for a in Degrees	tan(a)=73.7/39.4	$\tan (a) = \frac{73.7}{39.4}$
52431	Find Amplitude, Period, and Phase Shift	y=1/4cos((2x)/7+1/3)	$y = \frac{1}{4} \cos (\frac{2 x}{7} + \frac{1}{3})$
52432	Solve for θ in Degrees	cos(theta)^2=1/2	$\cos^{2} (θ) = \frac{1}{2}$
52433	Convert to Trigonometric Form	tan(90-theta)	$\tan (90 - θ)$
52434	Verify the Identity	x^3-2=(x- cube root of 2)(x^2+ cube root of 2x+ cube root of 4)	$x^{3} - 2 = (x - \sqrt[3]{2}) (x^{2} + \sqrt[3]{2} x + \sqrt[3]{4})$
52435	Find Amplitude, Period, and Phase Shift	y=4cos(3pix+2/5)	$y = 4 \cos (3 π x + \frac{2}{5})$
52436	Solve for θ in Degrees	sec(theta)^2-9=0	$\sec^{2} (θ) - 9 = 0$
52437	Solve for θ in Radians	cos(2theta-pi/2)=-1	$\cos (2 θ - \frac{π}{2}) = - 1$
52438	Find Amplitude, Period, and Phase Shift	y=3sin(theta/4)-2	$y = 3 \sin (\frac{θ}{4}) - 2$
52439	Solve for A in Degrees	5cos(A)+8=3cos(A)+6	$5 \cos (A) + 8 = 3 \cos (A) + 6$
52440	Find Amplitude, Period, and Phase Shift	f(x)=-1/2cos(4(x+pi/4))+1	$f (x) = - \frac{1}{2} \cos (4 (x + \frac{π}{4})) + 1$
52441	Find Amplitude, Period, and Phase Shift	y=-2cos(2x+pi)-1	$y = - 2 \cos (2 x + π) - 1$
52442	Find Amplitude, Period, and Phase Shift	y=-5tan(3x+pi)	$y = - 5 \tan (3 x + π)$
52443	Find Amplitude, Period, and Phase Shift	y=1/2cos((4pix)/5-5pi)	$y = \frac{1}{2} \cos (\frac{4 π x}{5} - 5 π)$
52444	Expand Using Sum/Difference Formulas	(2x+5)(2x-5)	$(2 x + 5) (2 x - 5)$
52445	Find the Cosine of the Angle	-(5pi)/6	$- \frac{5 π}{6}$
52446	Find the Cotangent Given the Point	( square root of 5,2)	$(\sqrt{5}, 2)$
52447	Find the Other Trig Values in Quadrant II	csc(theta) = square root of 2	$\csc (θ) = \sqrt{2}$
52448	Find the Reference Angle	cot(-pi/4)	$\cot (- \frac{π}{4})$
52449	Find the Cosine of the Angle	-pi/6	$- \frac{π}{6}$
52450	Convert from Radians to Degrees	arctan(-1/( square root of 3))	$\arctan (- \frac{1}{\sqrt{3}})$
52451	Solve for x in Degrees	4sin(x)cos(x)+cos(x)=0	$4 \sin (x) \cos (x) + \cos (x) = 0$
52452	Find Trig Functions Using Identities	tan(theta)=-3/5 , sec(theta)>0	$\tan (θ) = - \frac{3}{5}$ , $\sec (θ) > 0$
52453	Solve for x in Degrees	2sin(x)- square root of 3=0	$2 \sin (x) - \sqrt{3} = 0$
52454	Convert from Radians to Degrees	3*180/pi	$3 \cdot \frac{180}{π}$
52455	Find the Other Trig Values in Quadrant II	sec(theta)=- square root of 5	$\sec (θ) = - \sqrt{5}$
52456	Find the Sine of the Angle	(7pi)/6	$\frac{7 π}{6}$
52457	Solve for x in Radians	csc(x)=- square root of 2	$\csc (x) = - \sqrt{2}$
52458	Verify the Identity	12 root of 16 = cube root of fourth root of 16	$\sqrt[12]{16} = \sqrt[3]{\sqrt[4]{16}}$
52459	Solve for θ in Degrees	6sin(theta)+7=0	$6 \sin (θ) + 7 = 0$
52460	Convert from Radians to Degrees	cos(pi/12)	$\cos (\frac{π}{12})$
52461	Verify the Identity	sin(x)^2=sin(x)^2	$\sin^{2} (x) = \sin^{2} (x)$
52462	Find the Reference Angle	cot(150 degrees )	$\cot (150 °)$
52463	Convert from Degrees to Radians	130deg	$130$ degrees
52464	Convert from Radians to Degrees	-2pirad	$- 2 π$ radians
52465	Find the Coterminal Angle	1740 degrees	$1740 °$
52466	Solve for x in Degrees	2sin(x)cos(x)=cos(x)	$2 \sin (x) \cos (x) = \cos (x)$
52467	Convert from Radians to Degrees	(2pi)/7rad	$\frac{2 π}{7}$ rad
52468	Solve for x in Degrees	7tan(x)sin(x)=-6sin(x)	$7 \tan (x) \sin (x) = - 6 \sin (x)$
52469	Find the Cotangent Given the Point	(1/5,-(2 square root of 6)/5)	$(\frac{1}{5}, - \frac{2 \sqrt{6}}{5})$
52470	Find the Length of c	tri{4}{}{}{}{3}{90}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = & 4 \\ c = \\ a = & 3 \end{matrix} & \begin{matrix} A = \\ B = \\ C = & 90 \end{matrix} \end{matrix}$
52471	Find the Length of a	tri{}{45}{5}{45}{}{90}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = & 5 \\ a = \end{matrix} & \begin{matrix} A = & 45 \\ B = & 45 \\ C = & 90 \end{matrix} \end{matrix}$
52472	Find the Trig Value	csc(theta)=5 with pi/2<theta<pi	$\csc (θ) = 5$ with $\frac{π}{2} < θ < π$
52473	Find the Cosine Given the Point	((2 square root of 5)/5,-( square root of 5)/5)	$(\frac{2 \sqrt{5}}{5}, - \frac{\sqrt{5}}{5})$
52474	Find Amplitude, Period, and Phase Shift	y=1/2cos(2x-pi)+2	$y = \frac{1}{2} \cos (2 x - π) + 2$
52475	Convert to Trigonometric Form	2sin(10 degrees )cos(10 degrees )	$2 \sin (10 °) \cos (10 °)$
52476	Convert from Radians to Degrees	-5pirad	$- 5 π$ radians
52477	Solve for C in Degrees	-5cos(C)-1=2cos(C)+3	$- 5 \cos (C) - 1 = 2 \cos (C) + 3$
52478	Find the Sine of the Angle	(5pi)/3	$\frac{5 π}{3}$
52479	Find the Tangent of the Angle	(5pi)/3	$\frac{5 π}{3}$
52480	Verify the Identity	2cot(x)csc(x)=1/(sec(x)-1)+1/(sec(x)+1)	$2 \cot (x) \csc (x) = \frac{1}{\sec (x) - 1} + \frac{1}{\sec (x) + 1}$
52481	Solve for x in Degrees	cos(x)+ square root of 3=-cos(x)	$\cos (x) + \sqrt{3} = - \cos (x)$
52482	Expand Using Sum/Difference Formulas	(3+4x)(3-4x)	$(3 + 4 x) (3 - 4 x)$
52483	Expand Using Sum/Difference Formulas	cos(60 degrees -45 degrees )	$\cos (60 ° - 45 °)$
52484	Solve for x in Degrees	tan(x)sin(x)+4sin(x)=0	$\tan (x) \sin (x) + 4 \sin (x) = 0$
52485	Solve for θ in Degrees	6tan(theta)^2-10tan(theta)+1=-5tan(theta)	$6 \tan^{2} (θ) - 10 \tan (θ) + 1 = - 5 \tan (θ)$
52486	Solve for θ in Degrees	6sin(theta)^2-17sin(theta)+14=-4sin(theta)+9	$6 \sin^{2} (θ) - 17 \sin (θ) + 14 = - 4 \sin (θ) + 9$
52487	Verify the Identity	(sin(x)^2-cos(x)^2)/(sin(x)-cos(x))=sin(x)+cos(x)	$\frac{\sin^{2} (x) - \cos^{2} (x)}{\sin (x) - \cos (x)} = \sin (x) + \cos (x)$
52488	Find the Secant Given the Point	(-2/7,(3 square root of 5)/7)	$(- \frac{2}{7}, \frac{3 \sqrt{5}}{7})$
52489	Convert from Radians to Degrees	2/3rad	$\frac{2}{3}$ rad
52490	Convert to Rectangular Coordinates	(6 square root of 3,(7pi)/6)	$(6 \sqrt{3}, \frac{7 π}{6})$
52491	Solve for θ in Degrees	8tan(theta)^2+10tan(theta)+10=7	$8 \tan^{2} (θ) + 10 \tan (θ) + 10 = 7$
52492	Solve for x in Radians	2sin(pi/3x) = square root of 2	$2 \sin (\frac{π}{3} x) = \sqrt{2}$
52493	Find the Reference Angle	cot(330 degrees )	$\cot (330 °)$
52494	Verify the Identity	(sin(x))(cot(x)+cos(x)tan(x))=cos(x)+sin(x)^2	$(\sin (x)) (\cot (x) + \cos (x) \tan (x)) = \cos (x) + \sin^{2} (x)$
52495	Solve for θ in Degrees	2cot(theta)-3=0	$2 \cot (θ) - 3 = 0$
52496	Find the Value Using the Unit Circle	cot(-(5pi)/4)	$\cot (- \frac{5 π}{4})$
52497	Find Amplitude, Period, and Phase Shift	y=1/2sin(1/2x+pi/2)	$y = \frac{1}{2} \sin (\frac{1}{2} x + \frac{π}{2})$
52498	Find the Other Trig Values in Quadrant I	sin(60 degrees )=( square root of 3)/2	$\sin (60 °) = \frac{\sqrt{3}}{2}$
52499	Verify the Identity	((1+cos(A))(1-cos(A)))/(sin(A))=sin(A)	$\frac{(1 + \cos (A)) (1 - \cos (A))}{\sin (A)} = \sin (A)$
52500	Find the Cosecant Given the Point	(- square root of 3,1)	$(- \sqrt{3}, 1)$