Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
51501	Simplify Using Half-Angle Formula	cos((7pi)/12)	$\cos (\frac{7 π}{12})$
51502	Find Amplitude, Period, and Phase Shift	y=2sin(3theta+(5pi)/3)+1	$y = 2 \sin (3 θ + \frac{5 π}{3}) + 1$
51503	Solve for x in Radians	cot(x)-1=0	$\cot (x) - 1 = 0$
51504	Solve for θ in Degrees	2sin(theta)^2-sin(theta)-1=0	$2 \sin^{2} (θ) - \sin (θ) - 1 = 0$
51505	Find Amplitude, Period, and Phase Shift	y=2/3cos(-pi/3x+2)	$y = \frac{2}{3} \cos (- \frac{π}{3} x + 2)$
51506	Solve for θ in Degrees	sin(theta)^2+sin(theta)=0	$\sin^{2} (θ) + \sin (θ) = 0$
51507	Find the Trig Values Using Angle B	tri{12}{}{13}{}{5}{}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = & 12 \\ c = & 13 \\ a = & 5 \end{matrix} & \begin{matrix} A = \\ B = \\ C = \end{matrix} \end{matrix}$
51508	Convert to Trigonometric Form	1+sin(x)	$1 + \sin (x)$
51509	Convert to Trigonometric Form	(cos(theta)^2)/(1-sin(theta))	$\frac{\cos^{2} (θ)}{1 - \sin (θ)}$
51510	Solve for x in Radians	3tan(x) = square root of 3	$3 \tan (x) = \sqrt{3}$
51511	Convert to Trigonometric Form	csc(x)-sin(x)	$\csc (x) - \sin (x)$
51512	Solve for θ in Degrees	cos(theta)=-1/3	$\cos (θ) = - \frac{1}{3}$
51513	Find the Reference Angle	7/4pi	$\frac{7}{4} π$
51514	Find the Cotangent Given the Point	(-1,0)	$(- 1, 0)$
51515	Convert from Degrees to Radians	30 degrees *pi/180	$30 ° \cdot \frac{π}{180}$
51516	Solve for θ in Degrees	sin(theta)^2+3sin(theta)-4=0	$\sin^{2} (θ) + 3 \sin (θ) - 4 = 0$
51517	Solve for θ in Degrees	tan(theta)=8/15	$\tan (θ) = \frac{8}{15}$
51518	Find the Trig Value	cos(theta)=-5/13 , theta	$\cos (θ) = - \frac{5}{13}$ , $θ$
51519	Find the Reference Angle	5/4pi	$\frac{5}{4} π$
51520	Find the Length of c	tri{8}{}{}{}{6}{}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = & 8 \\ c = \\ a = & 6 \end{matrix} & \begin{matrix} A = \\ B = \\ C = \end{matrix} \end{matrix}$
51521	Solve for θ in Degrees	tan(theta)=5/4	$\tan (θ) = \frac{5}{4}$
51522	Find the Cotangent Given the Point	(8/17,-15/17)	$(\frac{8}{17}, - \frac{15}{17})$
51523	Solve for x in Radians	cos(4x)-1=0	$\cos (4 x) - 1 = 0$
51524	Solve for x in Radians	tan(x)=-2	$\tan (x) = - 2$
51525	Solve for x in Radians	4cos(x)^2-2=0	$4 \cos^{2} (x) - 2 = 0$
51526	Find the Coterminal Angle	660	$660$
51527	Solve for x in Degrees	cos(x)=12/13	$\cos (x) = \frac{12}{13}$
51528	Verify the Identity	1+x+(x^2)/(1-x)=1/(1-x)	$1 + x + \frac{x^{2}}{1 - x} = \frac{1}{1 - x}$
51529	Solve for θ in Radians	-2sin(theta)^2+cos(theta)+1=0	$- 2 \sin^{2} (θ) + \cos (θ) + 1 = 0$
51530	Solve for θ in Radians	-2cos(theta)^2+sin(theta)+1=0	$- 2 \cos^{2} (θ) + \sin (θ) + 1 = 0$
51531	Verify the Identity	1-cos(x)^2=(cos(x)sin(x))/(cot(x))	$1 - \cos^{2} (x) = \frac{\cos (x) \sin (x)}{\cot (x)}$
51532	Convert from Radians to Degrees	10/9pirad	$\frac{10}{9} π$ rad
51533	Verify the Identity	(sin(-x))/(cos(-x)tan(-x))=1	$\frac{\sin (- x)}{\cos (- x) \tan (- x)} = 1$
51534	Solve for x in Degrees	3cos(x)=3+7cos(x)	$3 \cos (x) = 3 + 7 \cos (x)$
51535	Find the Coterminal Angle	-1323 degrees	$- 1323 °$
51536	Find Amplitude, Period, and Phase Shift	y=2cos(3x-pi)+4	$y = 2 \cos (3 x - π) + 4$
51537	Find Amplitude, Period, and Phase Shift	y=-4sin(x+3pi)	$y = - 4 \sin (x + 3 π)$
51538	Verify the Identity	1/(1+sec(s))+1/(1-sec(s))=-2cot(s)^2	$\frac{1}{1 + \sec (s)} + \frac{1}{1 - \sec (s)} = - 2 \cot^{2} (s)$
51539	Solve for θ in Radians	cos(theta)+sin(theta)*tan(theta)=2	$\cos (θ) + \sin (θ) \cdot \tan (θ) = 2$
51540	Find Amplitude, Period, and Phase Shift	y=-sin((6x)/5-(2pi)/3)	$y = - \sin (\frac{6 x}{5} - \frac{2 π}{3})$
51541	Find Amplitude, Period, and Phase Shift	y=cos((5x)/3-7/9)-10	$y = \cos (\frac{5 x}{3} - \frac{7}{9}) - 10$
51542	Expand Using Sum/Difference Formulas	2x(5x-2)	$2 x (5 x - 2)$
51543	Find Amplitude, Period, and Phase Shift	y=2-2/3cos(x-pi/2)	$y = 2 - \frac{2}{3} \cos (x - \frac{π}{2})$
51544	Find Trig Functions Using Identities	sin(theta)=-1 , cot(theta)=0	$\sin (θ) = - 1$ , $\cot (θ) = 0$
51545	Solve for θ in Radians	sin(theta)+cos(theta)*cot(theta)=2	$\sin (θ) + \cos (θ) \cdot \cot (θ) = 2$
51546	Find Trig Functions Using Identities	sin(x)=( square root of 3)/2 , cos(x)=-1/2	$\sin (x) = \frac{\sqrt{3}}{2}$ , $\cos (x) = - \frac{1}{2}$
51547	Find Amplitude, Period, and Phase Shift	f(t)=-3sin(1/2x-2pi)	$f (t) = - 3 \sin (\frac{1}{2} x - 2 π)$
51548	Find Amplitude, Period, and Phase Shift	f(t)=-6sin(3/2x+4pi)	$f (t) = - 6 \sin (\frac{3}{2} x + 4 π)$
51549	Verify the Identity	1=sec(x)^2cos(x)^2	$1 = \sec^{2} (x) \cos^{2} (x)$
51550	Verify the Identity	(cos(theta)^2-sin(theta)^2)/(cos(theta)+sin(theta))=cos(theta)-sin(theta)	$\frac{\cos^{2} (θ) - \sin^{2} (θ)}{\cos (θ) + \sin (θ)} = \cos (θ) - \sin (θ)$
51551	Verify the Identity	sec(theta)cos(theta)+sec(theta)sin(theta)=1+tan(theta)	$\sec (θ) \cos (θ) + \sec (θ) \sin (θ) = 1 + \tan (θ)$
51552	Verify the Identity	(1- square root of x)/(1+ square root of x)=(1-2 square root of x+x)/(1-x)	$\frac{1 - \sqrt{x}}{1 + \sqrt{x}} = \frac{1 - 2 \sqrt{x} + x}{1 - x}$
51553	Find the Other Trig Values in Quadrant IV	cos(2A)=5/8	$\cos (2 A) = \frac{5}{8}$
51554	Find Amplitude, Period, and Phase Shift	y=sin(2/3x-pi/2)-11	$y = \sin (\frac{2}{3} x - \frac{π}{2}) - 11$
51555	Find Amplitude, Period, and Phase Shift	y=-2cos(-x/2)	$y = - 2 \cos (- \frac{x}{2})$
51556	Convert from Radians to Degrees	(11pi)/6rad	$\frac{11 π}{6}$ radians
51557	Solve for θ in Degrees	csc(theta)=-1	$\csc (θ) = - 1$
51558	Find Amplitude, Period, and Phase Shift	y=3/2cos((pix)/2)	$y = \frac{3}{2} \cos (\frac{π x}{2})$
51559	Find Amplitude, Period, and Phase Shift	y=2sin(-3theta-pi/2)+2	$y = 2 \sin (- 3 θ - \frac{π}{2}) + 2$
51560	Find Amplitude, Period, and Phase Shift	y=3cos(x/10-pi/12)	$y = 3 \cos (\frac{x}{10} - \frac{π}{12})$
51561	Find the Coterminal Angle	3pi	$3 π$
51562	Find the Cotangent Given the Point	(-1, square root of 3)	$(- 1, \sqrt{3})$
51563	Convert from Radians to Degrees	pi/9rad	$\frac{π}{9}$ radians
51564	Verify the Identity	cot(theta)sin(theta)cos(theta)=1-sin(theta)^2	$\cot (θ) \sin (θ) \cos (θ) = 1 - \sin^{2} (θ)$
51565	Expand Using Sum/Difference Formulas	4p(p-7q)	$4 p (p - 7 q)$
51566	Verify the Identity	csc(theta)^2*tan(theta)^2-1=tan(theta)^2	$\csc^{2} (θ) \cdot \tan^{2} (θ) - 1 = \tan^{2} (θ)$
51567	Verify the Identity	sin(t)^2+(cos(t)^2-tan(t)^2)=1-tan(t)^2	$\sin^{2} (t) + (\cos^{2} (t) - \tan^{2} (t)) = 1 - \tan^{2} (t)$
51568	Find the Trig Value	cos(theta)=-5/13 and pi/2<theta<pi	$\cos (θ) = - \frac{5}{13}$ and $\frac{π}{2} < θ < π$
51569	Find the Cotangent Given the Point	(1,- square root of 3)	$(1, - \sqrt{3})$
51570	Verify the Identity	square root of sin(x)^2+cos(x)^2=1	$\sqrt{\sin^{2} (x) + \cos^{2} (x)} = 1$
51571	Expand Using Sum/Difference Formulas	2x(3x+2y)	$2 x (3 x + 2 y)$
51572	Solve for θ in Degrees	sec(theta)=1	$\sec (θ) = 1$
51573	Verify the Identity	(2sin(t)cos(t))/(sin(t)+cos(t))=sin(t)+cos(t)-1/(sin(t)+cos(t))	$\frac{2 \sin (t) \cos (t)}{\sin (t) + \cos (t)} = \sin (t) + \cos (t) - \frac{1}{\sin (t) + \cos (t)}$
51574	Find the Reference Angle	sin(510 degrees )	$\sin (510 °)$
51575	Find Amplitude, Period, and Phase Shift	y=-4sin(x+6pi)-8	$y = - 4 \sin (x + 6 π) - 8$
51576	Verify the Identity	square root of x^2=x	$\sqrt{x^{2}} = x$
51577	Convert from Radians to Degrees	7rad	$7$ radians
51578	Find the Trig Value	cos(theta)=-3/5 ; and pi/2<theta<pi	$\cos (θ) = - \frac{3}{5}$ ; and $\frac{π}{2} < θ < π$
51579	Convert from Radians to Degrees	(29pi)/6rad	$\frac{29 π}{6}$ rad
51580	Find Amplitude, Period, and Phase Shift	y=-3/2sin(x/3+pi/6)+2	$y = - \frac{3}{2} \sin (\frac{x}{3} + \frac{π}{6}) + 2$
51581	Find the Coterminal Angle	-1400 degrees	$- 1400 °$
51582	Find the Cosecant Given the Point	(-1, square root of 3)	$(- 1, \sqrt{3})$
51583	Find the Reference Angle	tan(pi/6)	$\tan (\frac{π}{6})$
51584	Find Trig Functions Using Identities	cos(theta)=0 , csc(theta)=1	$\cos (θ) = 0$ , $\csc (θ) = 1$
51585	Convert from Radians to Degrees	(4pi)/3rad	$\frac{4 π}{3}$ radians
51586	Verify the Identity	2sin(t)cos(t)+1=((sec(t)+csc(t))/(sec(t)csc(t)))^2	$2 \sin (t) \cos (t) + 1 = {(\frac{\sec (t) + \csc (t)}{\sec (t) \csc (t)})}^{2}$
51587	Find the Value Using the Unit Circle	cot(45 degrees )	$\cot (45 °)$
51588	Find the Other Trig Values in Quadrant IV	sin(theta)=0	$\sin (θ) = 0$
51589	Expand Using Sum/Difference Formulas	5(2x-1)	$5 (2 x - 1)$
51590	Verify the Identity	1/(sin(x)(1-cos(x)))=(cos(x)+1)/(sin(x)^3)	$\frac{1}{\sin (x) (1 - \cos (x))} = \frac{(\cos (x) + 1)}{\sin^{3} (x)}$
51591	Expand the Trigonometric Expression	(1+cos(2y))/(sin(2y))	$\frac{1 + \cos (2 y)}{\sin (2 y)}$
51592	Verify the Identity	cos(A+B)=cos(A)cos(B)-sin(A)sin(B)	$\cos (A + B) = \cos (A) \cos (B) - \sin (A) \sin (B)$
51593	Find Amplitude, Period, and Phase Shift	y=2cot(1/2theta)+1	$y = 2 \cot (\frac{1}{2} θ) + 1$
51594	Convert from Radians to Degrees	10rad	$10$ rad
51595	Convert from Radians to Degrees	2.32rad	$2.32$ rad
51596	Find the Coterminal Angle	5pi	$5 π$
51597	Find Angle A	tri{}{}{}{}{}{}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = \\ a = \end{matrix} & \begin{matrix} A = \\ B = \\ C = \end{matrix} \end{matrix}$
51598	Expand Using Sum/Difference Formulas	3(x+4)	$3 (x + 4)$
51599	Find the Reference Angle	tan(405 degrees )	$\tan (405 °)$
51600	Find the Reference Angle	cos(pi/3)	$\cos (\frac{π}{3})$