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Trigonometry

Rank	Topic	Problem	Formatted Problem
52301	Solve for θ in Degrees	sec(theta)^2-6sec(theta)+8=0	$\sec^{2} (θ) - 6 \sec (θ) + 8 = 0$
52302	Find Amplitude, Period, and Phase Shift	f(x)=sin(pi/3x+pi)	$f (x) = \sin (\frac{π}{3} x + π)$
52303	Convert to Rectangular Coordinates	( square root of 3,pi)	$(\sqrt{3}, π)$
52304	Find Amplitude, Period, and Phase Shift	f(x)=2sec(2x)+1	$f (x) = 2 \sec (2 x) + 1$
52305	Find the Coterminal Angle	-2/5pi	$- \frac{2}{5} π$
52306	Solve for A in Degrees	10sin(A)+16=3sin(A)+9	$10 \sin (A) + 16 = 3 \sin (A) + 9$
52307	Solve for θ in Degrees	tan(theta)-5=4tan(theta)-5	$\tan (θ) - 5 = 4 \tan (θ) - 5$
52308	Find the Sine Given the Point	((2 square root of 13)/13,-(3 square root of 13)/13)	$(\frac{2 \sqrt{13}}{13}, - \frac{3 \sqrt{13}}{13})$
52309	Find the Cosine Given the Point	((2 square root of 13)/13,-(3 square root of 13)/13)	$(\frac{2 \sqrt{13}}{13}, - \frac{3 \sqrt{13}}{13})$
52310	Solve for a in Degrees	tan(a)=2.0503	$\tan (a) = 2.0503$
52311	Find the Secant Given the Point	(-1/5,(2 square root of 6)/5)	$(- \frac{1}{5}, \frac{2 \sqrt{6}}{5})$
52312	Find Amplitude, Period, and Phase Shift	y=4sin((4pix)/5-3)	$y = 4 \sin (\frac{4 π x}{5} - 3)$
52313	Find the Trig Value	cot(theta)=5/12 , csc(theta)	$\cot (θ) = \frac{5}{12}$ , $\csc (θ)$
52314	Solve for x in Degrees	7cos(x)sin(x)=-sin(x)	$7 \cos (x) \sin (x) = - \sin (x)$
52315	Solve for θ in Degrees	cot(theta)^2-9=0	$\cot^{2} (θ) - 9 = 0$
52316	Find Amplitude, Period, and Phase Shift	y=cos(2(theta-pi))	$y = \cos (2 (θ - π))$
52317	Expand Using Sum/Difference Formulas	log base x of 3m(4n)	$\log_{x} (3 m) (4 n)$
52318	Convert from Radians to Degrees	pi/3*180/pi	$\frac{π}{3} \cdot \frac{180}{π}$
52319	Find the Trig Value	tan(theta)=4/3 , 0<=theta<=pi/2	$\tan (θ) = \frac{4}{3}$ , $0 \leq θ \leq \frac{π}{2}$
52320	Solve for θ in Degrees	2tan(theta)^2-5tan(theta)+4=-8tan(theta)+6	$2 \tan^{2} (θ) - 5 \tan (θ) + 4 = - 8 \tan (θ) + 6$
52321	Find Amplitude, Period, and Phase Shift	y=sin((2x)/7+(3pi)/2)	$y = \sin (\frac{2 x}{7} + \frac{3 π}{2})$
52322	Find Amplitude, Period, and Phase Shift	f(x)=2*cos(8/3x)	$f (x) = 2 \cdot \cos (\frac{8}{3} x)$
52323	Convert to Trigonometric Form	(1-sin(x))/(cos(x))	$\frac{1 - \sin (x)}{\cos (x)}$
52324	Solve for x in Radians	csc(x) = square root of 2	$\csc (x) = \sqrt{2}$
52325	Find Amplitude, Period, and Phase Shift	y=1/4cos((4x)/7+(5pi)/6)	$y = \frac{1}{4} \cos (\frac{4 x}{7} + \frac{5 π}{6})$
52326	Verify	tan(x)+cot(x)=sec(x)csc(x)	$\tan (x) + \cot (x) = \sec (x) \csc (x)$
52327	Solve for θ in Radians	sin(2theta)+ square root of 2cos(theta)=0	$\sin (2 θ) + \sqrt{2} \cos (θ) = 0$
52328	Solve for θ in Radians	cos(theta)=(- square root of 3)/2	$\cos (θ) = \frac{- \sqrt{3}}{2}$
52329	Expand the Trigonometric Expression	tan(90-theta)	$\tan (90 - θ)$
52330	Convert from Radians to Degrees	3.26pirad	$3.26 π$ rad
52331	Expand Using Sum/Difference Formulas	(x+3)(x+5)	$(x + 3) (x + 5)$
52332	Find the Tangent of the Angle	pi/4	$\frac{π}{4}$
52333	Solve for x in Degrees	5cos(x)tan(x)=9tan(x)	$5 \cos (x) \tan (x) = 9 \tan (x)$
52334	Verify the Identity	(c-s)(c+s)=c^2-s^2	$(c - s) (c + s) = c^{2} - s^{2}$
52335	Find the Secant Given the Point	((3 square root of 13)/13,-(2 square root of 13)/13)	$(\frac{3 \sqrt{13}}{13}, - \frac{2 \sqrt{13}}{13})$
52336	Solve for x in Degrees	sec(x)=-2	$\sec (x) = - 2$
52337	Find the Cosine of the Angle	-pi/2	$- \frac{π}{2}$
52338	Solve for θ in Degrees	2sin(theta)^2=sin(theta)	$2 \sin^{2} (θ) = \sin (θ)$
52339	Convert to Trigonometric Form	(6(cos(pi/3)+isin(pi/3)))/(3(cos(pi/6)+isin(pi/6)))	$\frac{6 (\cos (\frac{π}{3}) + i \sin (\frac{π}{3}))}{3 (\cos (\frac{π}{6}) + i \sin (\frac{π}{6}))}$
52340	Find the Reference Angle	cot(225 degrees )	$\cot (225 °)$
52341	Find the Length of c	tri{}{30}{}{60}{12}{90}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = \\ a = & 12 \end{matrix} & \begin{matrix} A = & 30 \\ B = & 60 \\ C = & 90 \end{matrix} \end{matrix}$
52342	Find Amplitude, Period, and Phase Shift	y=5sin(2/3x-2/9pi)	$y = 5 \sin (\frac{2}{3} x - \frac{2}{9} π)$
52343	Solve for θ in Radians	2sin(theta)+4=4	$2 \sin (θ) + 4 = 4$
52344	Expand Using Sum/Difference Formulas	cos(x-pi/4)	$\cos (x - \frac{π}{4})$
52345	Solve for x in Radians	square root of 3cot(x)+1=0	$\sqrt{3} \cot (x) + 1 = 0$
52346	Solve for x in Degrees	8tan(x)sin(x)=sin(x)	$8 \tan (x) \sin (x) = \sin (x)$
52347	Solve for θ in Degrees	2cos(2theta)^2=1-cos(2theta)	$2 \cos^{2} (2 θ) = 1 - \cos (2 θ)$
52348	Convert to Rectangular Coordinates	(8,15 degrees )	$(8, 15 °)$
52349	Solve for θ in Degrees	cos(theta)^2+cos(theta)=0	$\cos^{2} (θ) + \cos (θ) = 0$
52350	Find Amplitude, Period, and Phase Shift	y=2cos(4pix-5)	$y = 2 \cos (4 π x - 5)$
52351	Find the Coterminal Angle	25pi	$25 π$
52352	Solve for θ in Degrees	sin(theta)^2-16=0	$\sin^{2} (θ) - 16 = 0$
52353	Convert to Trigonometric Form	cos(x+y)	$\cos (x + y)$
52354	Find Amplitude, Period, and Phase Shift	y=3sin(2pix+4)	$y = 3 \sin (2 π x + 4)$
52355	Convert from Radians to Degrees	arctan(( square root of 3)/1)	$\arctan (\frac{\sqrt{3}}{1})$
52356	Solve for θ in Degrees	-270=1900sin(theta)	$- 270 = 1900 \sin (θ)$
52357	Convert from Radians to Degrees	arcsin(-3/5)	$\arcsin (- \frac{3}{5})$
52358	Find Trig Functions Using Identities	sec(x)=-5/2 , tan(x)<0	$\sec (x) = - \frac{5}{2}$ , $\tan (x) < 0$
52359	Find Trig Functions Using Identities	tan(theta)=3/4 , sin(theta)>0	$\tan (θ) = \frac{3}{4}$ , $\sin (θ) > 0$
52360	Find Amplitude, Period, and Phase Shift	y=sin((3pix)/2-3/5)	$y = \sin (\frac{3 π x}{2} - \frac{3}{5})$
52361	Find the Cosine of the Angle	225 degrees	$225 °$
52362	Find the Reference Angle	sin((11pi)/4)	$\sin (\frac{11 π}{4})$
52363	Convert from Degrees to Radians	( square root of 3)/2	$\frac{\sqrt{3}}{2}$
52364	Find the Cosecant Given the Point	(2/19,y)	$(\frac{2}{19}, y)$
52365	Solve for θ in Radians	sec(theta)+1=0	$\sec (θ) + 1 = 0$
52366	Expand Using Sum/Difference Formulas	(4+x)(4-x)	$(4 + x) (4 - x)$
52367	Verify the Identity	(x+3)^2(x^3+3x^2+3x+1)=(x^2+6x+9)(x+1)^3	${(x + 3)}^{2} (x^{3} + 3 x^{2} + 3 x + 1) = (x^{2} + 6 x + 9) {(x + 1)}^{3}$
52368	Find the Reference Angle	cos(-(7pi)/6)	$\cos (- \frac{7 π}{6})$
52369	Convert from Degrees to Radians	45 degrees *pi/180 degrees	$45 ° \cdot \frac{π}{180 °}$
52370	Find Amplitude, Period, and Phase Shift	y=1/3cos(2x+4pi)	$y = \frac{1}{3} \cos (2 x + 4 π)$
52371	Expand Using Sum/Difference Formulas	cos(270 degrees -theta)	$\cos (270 ° - θ)$
52372	Solve for x in Degrees	sec(x) = square root of 2	$\sec (x) = \sqrt{2}$
52373	Find Amplitude, Period, and Phase Shift	y=4cos((4pix)/7+5)	$y = 4 \cos (\frac{4 π x}{7} + 5)$
52374	Convert from Radians to Degrees	-20rad	$- 20$ rad
52375	Solve for x in Radians	cos(x)=0.5	$\cos (x) = 0.5$
52376	Find Amplitude, Period, and Phase Shift	y=cos((4pix)/7-2pi)	$y = \cos (\frac{4 π x}{7} - 2 π)$
52377	Solve for x in Radians	2sin(x)^2-5sin(x)+2=0	$2 \sin^{2} (x) - 5 \sin (x) + 2 = 0$
52378	Convert from Radians to Degrees	2/(3pi)	$\frac{2}{3 π}$
52379	Verify the Identity	x^2-y^2=(x-y)(x+y)	$x^{2} - y^{2} = (x - y) (x + y)$
52380	Verify the Identity	(2+csc(A))/(sec(A))-2cos(A)=cot(A)	$\frac{2 + \csc (A)}{\sec (A)} - 2 \cos (A) = \cot (A)$
52381	Expand Using Sum/Difference Formulas	sin(pi/4-B)	$\sin (\frac{π}{4} - B)$
52382	Solve for x in Degrees	3cos(x)tan(x)=-5tan(x)	$3 \cos (x) \tan (x) = - 5 \tan (x)$
52383	Verify the Identity	sec(x)^2+cot(x)^2=tan(x)^2+csc(x)^2	$\sec^{2} (x) + \cot^{2} (x) = \tan^{2} (x) + \csc^{2} (x)$
52384	Verify the Identity	(sin(theta))/(1+cos(theta))*(1-cos(theta))/(1-cos(theta))=(1-cos(theta))/(sin(theta))	$\frac{\sin (θ)}{1 + \cos (θ)} \cdot \frac{1 - \cos (θ)}{1 - \cos (θ)} = \frac{1 - \cos (θ)}{\sin (θ)}$
52385	Solve for x in Radians	( square root of 2)/2csc(x)-1=0	$\frac{\sqrt{2}}{2} \csc (x) - 1 = 0$
52386	Find the Reference Angle	cot(-pi/3)	$\cot (- \frac{π}{3})$
52387	Find the Length of a	tri{}{30}{10}{60}{}{90}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = & 10 \\ a = \end{matrix} & \begin{matrix} A = & 30 \\ B = & 60 \\ C = & 90 \end{matrix} \end{matrix}$
52388	Solve for θ in Degrees	cos(theta)=sin(theta)	$\cos (θ) = \sin (θ)$
52389	Solve for A in Degrees	-6cos(A)+8=3cos(A)+8	$- 6 \cos (A) + 8 = 3 \cos (A) + 8$
52390	Find the Reference Angle	(-(7pi)/6)	$(- \frac{7 π}{6})$
52391	Expand Using Sum/Difference Formulas	2(y+5x)	$2 (y + 5 x)$
52392	Solve for x in Degrees	cos(x)sin(x)+sin(x)=0	$\cos (x) \sin (x) + \sin (x) = 0$
52393	Find the Cosine of the Angle	2pi	$2 π$
52394	Expand Using Sum/Difference Formulas	tan(pi/4+x)	$\tan (\frac{π}{4} + x)$
52395	Find Amplitude, Period, and Phase Shift	y=3-2cos(x/2)	$y = 3 - 2 \cos (\frac{x}{2})$
52396	Find the Reference Angle	-135deg	$- 135$ degrees
52397	Find Amplitude, Period, and Phase Shift	y=1/2cos((pix)/3-3/5)	$y = \frac{1}{2} \cos (\frac{π x}{3} - \frac{3}{5})$
52398	Find the Reference Angle	cot((41pi)/6)	$\cot (\frac{41 π}{6})$
52399	Solve for θ in Degrees	csc(theta)^2-4=0	$\csc^{2} (θ) - 4 = 0$
52400	Find the Cotangent of the Angle	(5pi)/6	$\frac{5 π}{6}$