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Trigonometry

Rank	Topic	Problem	Formatted Problem
52101	Verify the Identity	sin(a)=tan(a)*cos(a)	$\sin (a) = \tan (a) \cdot \cos (a)$
52102	Solve for θ in Degrees	16sec(theta)^2-1=0	$16 \sec^{2} (θ) - 1 = 0$
52103	Verify the Identity	(sec(x)^2-tan(x)^2+tan(x))/(sec(x))=sin(x)+cos(x)	$\frac{\sec^{2} (x) - \tan^{2} (x) + \tan (x)}{\sec (x)} = \sin (x) + \cos (x)$
52104	Find the Cosine of the Angle	-(4pi)/3	$- \frac{4 π}{3}$
52105	Find Amplitude, Period, and Phase Shift	y=-1/2cos(x-pi)	$y = - \frac{1}{2} \cos (x - π)$
52106	Find Amplitude, Period, and Phase Shift	y=-2-4sin(pi/2(x-1/3))	$y = - 2 - 4 \sin (\frac{π}{2} (x - \frac{1}{3}))$
52107	Solve for x in Radians	cos(x)-sin(x)=0	$\cos (x) - \sin (x) = 0$
52108	Find Amplitude, Period, and Phase Shift	y=3sin(pix-1/2)	$y = 3 \sin (π x - \frac{1}{2})$
52109	Find the Cosecant Given the Point	((3 square root of 13)/13,-(2 square root of 13)/13)	$(\frac{3 \sqrt{13}}{13}, - \frac{2 \sqrt{13}}{13})$
52110	Find the Other Trig Values in Quadrant III	cos(theta)=0	$\cos (θ) = 0$
52111	Find the Reference Angle	cos((13pi)/3)	$\cos (\frac{13 π}{3})$
52112	Solve for x in Radians	sin(2x)=-sin(x)	$\sin (2 x) = - \sin (x)$
52113	Find Amplitude, Period, and Phase Shift	y=3sin(100x+1)	$y = 3 \sin (100 x + 1)$
52114	Convert to Trigonometric Form	(1-cos(2x))/(sin(2x))	$\frac{1 - \cos (2 x)}{\sin (2 x)}$
52115	Solve for B in Degrees	3sin(B)+3=5sin(B)+2	$3 \sin (B) + 3 = 5 \sin (B) + 2$
52116	Find Amplitude, Period, and Phase Shift	f(x)=-2*cos(x)	$f (x) = - 2 \cdot \cos (x)$
52117	Solve for A in Degrees	-2cos(A)+6=cos(A)+9	$- 2 \cos (A) + 6 = \cos (A) + 9$
52118	Find the Cotangent Given the Point	( square root of 7,3)	$(\sqrt{7}, 3)$
52119	Find Amplitude, Period, and Phase Shift	y=3csc(theta/4+5)	$y = 3 \csc (\frac{θ}{4} + 5)$
52120	Find Trig Functions Using Identities	tan(theta)=-1/3 , sin(theta)>0	$\tan (θ) = - \frac{1}{3}$ , $\sin (θ) > 0$
52121	Expand Using Sum/Difference Formulas	3(x+5)	$3 (x + 5)$
52122	Verify the Identity	(csc(theta)^2)/(csc(theta)^2-1)=sec(theta)^2	$\frac{\csc^{2} (θ)}{\csc^{2} (θ) - 1} = \sec^{2} (θ)$
52123	Expand Using Sum/Difference Formulas	csc(90-theta)	$\csc (90 - θ)$
52124	Convert from Radians to Degrees	13rad	$13$ radians
52125	Verify the Identity	3(x+1)=3x+3	$3 (x + 1) = 3 x + 3$
52126	Convert from Radians to Degrees	pi/1	$\frac{π}{1}$
52127	Convert to Trigonometric Form	(sin(t))/(sec(t)-cos(t))	$\frac{\sin (t)}{\sec (t) - \cos (t)}$
52128	Solve for x in Radians	sec(x)=- square root of 2	$\sec (x) = - \sqrt{2}$
52129	Find the Reference Angle	cot(240 degrees )	$\cot (240 °)$
52130	Convert from Degrees to Radians	-315deg	$- 315$ degrees
52131	Convert to Trigonometric Form	sin(x)cos(x)	$\sin (x) \cos (x)$
52132	Convert from Radians to Degrees	-(2 square root of 3)/3	$- \frac{2 \sqrt{3}}{3}$
52133	Find Amplitude, Period, and Phase Shift	y=4sin((x-pi)/4)-3	$y = 4 \sin (\frac{x - π}{4}) - 3$
52134	Solve for c in Degrees	-3tan(c)+3=tan(c)-1	$- 3 \tan (c) + 3 = \tan (c) - 1$
52135	Find Amplitude, Period, and Phase Shift	y=sin(2(theta+pi))	$y = \sin (2 (θ + π))$
52136	Find the Other Trig Values in Quadrant IV	sec(theta)=(2 square root of 3)/3	$\sec (θ) = \frac{2 \sqrt{3}}{3}$
52137	Solve for θ in Degrees	tan(theta)^2+6tan(theta)+8=0	$\tan^{2} (θ) + 6 \tan (θ) + 8 = 0$
52138	Find Amplitude, Period, and Phase Shift	y=4sin(3(x-2))+5	$y = 4 \sin (3 (x - 2)) + 5$
52139	Find the Length of b	tri{}{45}{6}{45}{}{90}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = & 6 \\ a = \end{matrix} & \begin{matrix} A = & 45 \\ B = & 45 \\ C = & 90 \end{matrix} \end{matrix}$
52140	Find Amplitude, Period, and Phase Shift	f(x)=-4-5cos(2x-pi)	$f (x) = - 4 - 5 \cos (2 x - π)$
52141	Find the Tangent Given the Point	(1,- square root of 3)	$(1, - \sqrt{3})$
52142	Find the Secant Given the Point	(- square root of 3,1)	$(- \sqrt{3}, 1)$
52143	Verify the Identity	tan(2x)^2+cos(2x)^2+sin(2x)^2=sec(2x)^2	$\tan^{2} (2 x) + \cos^{2} (2 x) + \sin^{2} (2 x) = \sec^{2} (2 x)$
52144	Expand Using Sum/Difference Formulas	-2.5(-3+4n+8)	$- 2.5 (- 3 + 4 n + 8)$
52145	Verify the Identity	cos(-theta)=cos(theta)	$\cos (- θ) = \cos (θ)$
52146	Convert to Rectangular Coordinates	(4 square root of 3,pi/3)	$(4 \sqrt{3}, \frac{π}{3})$
52147	Find the Secant Given the Point	( square root of 5,2)	$(\sqrt{5}, 2)$
52148	Find the Reference Angle	cot(120 degrees )	$\cot (120 °)$
52149	Solve for C in Degrees	12sin(C)+6=5sin(C)+6	$12 \sin (C) + 6 = 5 \sin (C) + 6$
52150	Solve for A in Degrees	-2tan(A)+2=4tan(A)+6	$- 2 \tan (A) + 2 = 4 \tan (A) + 6$
52151	Find Amplitude, Period, and Phase Shift	y=-2sin(3x-(3pi)/4)+2	$y = - 2 \sin (3 x - \frac{3 π}{4}) + 2$
52152	Solve for B in Degrees	12tan(B)+5=5tan(B)+5	$12 \tan (B) + 5 = 5 \tan (B) + 5$
52153	Solve for θ in Degrees	4sin(theta)^2=1	$4 \sin^{2} (θ) = 1$
52154	Find Amplitude, Period, and Phase Shift	y=-4sin(x/3)-1	$y = - 4 \sin (\frac{x}{3}) - 1$
52155	Find the Reference Angle	cot(-225 degrees )	$\cot (- 225 °)$
52156	Solve for θ in Degrees	25csc(theta)^2-4=0	$25 \csc^{2} (θ) - 4 = 0$
52157	Convert from Radians to Degrees	5pirad	$5 π$ rad
52158	Convert from Radians to Degrees	8rad	$8$ rad
52159	Find Amplitude, Period, and Phase Shift	y=sin(x-pi)-1	$y = \sin (x - π) - 1$
52160	Find Amplitude, Period, and Phase Shift	y=2/3cos((x-3)/4)+1	$y = \frac{2}{3} \cos (\frac{x - 3}{4}) + 1$
52161	Find the Reference Angle	tan(pi/2)	$\tan (\frac{π}{2})$
52162	Convert to Trigonometric Form	3(cos(pi)+isin(pi))	$3 (\cos (π) + i \sin (π))$
52163	Find the Coterminal Angle	11/4pi	$\frac{11}{4} π$
52164	Solve for θ in Degrees	16sec(theta)^2-25=0	$16 \sec^{2} (θ) - 25 = 0$
52165	Find the Cosecant Given the Point	(-5/9,(2 square root of 14)/9)	$(- \frac{5}{9}, \frac{2 \sqrt{14}}{9})$
52166	Verify the Identity	sin(theta)^2sec(theta)^2=sec(theta)^2-1	$\sin^{2} (θ) \sec^{2} (θ) = \sec^{2} (θ) - 1$
52167	Solve the Triangle	B=30 degrees , C=43 degrees ; and a=8	$B = 30 °$ , $C = 43 °$ ; and $a = 8$
52168	Find the Value Using the Unit Circle	cot(135 degrees )	$\cot (135 °)$
52169	Find Amplitude, Period, and Phase Shift	y=6sin(pix-6)-6	$y = 6 \sin (π x - 6) - 6$
52170	Convert from Radians to Degrees	arcsin(2.5/5)	$\arcsin (\frac{2.5}{5})$
52171	Find the Sine Given the Point	((2 square root of 5)/5,-( square root of 5)/5)	$(\frac{2 \sqrt{5}}{5}, - \frac{\sqrt{5}}{5})$
52172	Find Amplitude, Period, and Phase Shift	y=sin(1/3(x-pi/6))	$y = \sin (\frac{1}{3} (x - \frac{π}{6}))$
52173	Find Amplitude, Period, and Phase Shift	y=2cos(pi/2x+pi/6)	$y = 2 \cos (\frac{π}{2} x + \frac{π}{6})$
52174	Find the Sine of the Angle	(4pi)/3	$\frac{4 π}{3}$
52175	Find Amplitude, Period, and Phase Shift	y=cos(x-2pi)-1	$y = \cos (x - 2 π) - 1$
52176	Find Amplitude, Period, and Phase Shift	y=-2sec(2x+pi/2)+7	$y = - 2 \sec (2 x + \frac{π}{2}) + 7$
52177	Find Amplitude, Period, and Phase Shift	y=2sin((8pix)/3+(3pi)/2)	$y = 2 \sin (\frac{8 π x}{3} + \frac{3 π}{2})$
52178	Solve for x in Radians	tan(x)^2=sec(x)-1	$\tan^{2} (x) = \sec (x) - 1$
52179	Find Amplitude, Period, and Phase Shift	y=4sin((8x)/5-pi/2)	$y = 4 \sin (\frac{8 x}{5} - \frac{π}{2})$
52180	Convert from Degrees to Radians	( square root of 2)/2	$\frac{\sqrt{2}}{2}$
52181	Convert from Radians to Degrees	(7pi)/5rad	$\frac{7 π}{5}$ radians
52182	Find Amplitude, Period, and Phase Shift	y=10sin((6pi)/4(x-pi/2))+25	$y = 10 \sin (\frac{6 π}{4} (x - \frac{π}{2})) + 25$
52183	Find Amplitude, Period, and Phase Shift	y=cos((2pix)/3+1/3)	$y = \cos (\frac{2 π x}{3} + \frac{1}{3})$
52184	Find Amplitude, Period, and Phase Shift	y=1/2sin(x-pi)+1	$y = \frac{1}{2} \sin (x - π) + 1$
52185	Find the Cotangent Given the Point	((4 square root of 3)/7,1/7)	$(\frac{4 \sqrt{3}}{7}, \frac{1}{7})$
52186	Find Amplitude, Period, and Phase Shift	f(x)=1-3sin(2x-9)	$f (x) = 1 - 3 \sin (2 x - 9)$
52187	Find Amplitude, Period, and Phase Shift	y=cos((6pix)/5+pi/3)	$y = \cos (\frac{6 π x}{5} + \frac{π}{3})$
52188	Find Amplitude, Period, and Phase Shift	y=2sin(4(x-1/2))+3	$y = 2 \sin (4 (x - \frac{1}{2})) + 3$
52189	Verify the Identity	sin(theta)csc(theta)=cos(theta)sec(theta)	$\sin (θ) \csc (θ) = \cos (θ) \sec (θ)$
52190	Solve for x in Degrees	csc(x)=(2 square root of 3)/3	$\csc (x) = \frac{2 \sqrt{3}}{3}$
52191	Convert from Radians to Degrees	sin(pi/3)	$\sin (\frac{π}{3})$
52192	Solve for θ in Radians	2sin(theta)^2=1	$2 \sin^{2} (θ) = 1$
52193	Find the Coterminal Angle	3998 degrees	$3998 °$
52194	Verify the Identity	(tan(x))/(1-tan(x)^2)=(sin(x)cos(x))/(2cos(x)^2-1)	$\frac{\tan (x)}{1 - \tan^{2} (x)} = \frac{\sin (x) \cos (x)}{2 \cos^{2} (x) - 1}$
52195	Find the Cosecant Given the Point	(-6,6)	$(- 6, 6)$
52196	Find the Other Trig Values in Quadrant IV	cos(theta)=0	$\cos (θ) = 0$
52197	Find the Coterminal Angle	(-17pi)/3	$\frac{- 17 π}{3}$
52198	Solve for x in Degrees	tan(x)+ square root of 3=0	$\tan (x) + \sqrt{3} = 0$
52199	Find the Tangent of the Angle	(11pi)/6	$\frac{11 π}{6}$
52200	Find the Reference Angle	tan((7pi)/4)	$\tan (\frac{7 π}{4})$