Rewrite the expression as a sum or difference: cos ⁡ 2 y ⋅ sin ⁡ 5 y \cos2y\ \cdot\sin\ 5y cos 2 y ⋅ sin 5 y

1 2 sin ⁡ 7 y + 1 2 sin ⁡ 3 y \frac{1}{2}\sin7y+\frac{1}{2}\sin3y 2 1 sin 7 y + 2 1 sin 3 y

1 2 sin ⁡ 7 y + sin ⁡ 3 y \frac{1}{2}\sin7y+\sin3y 2 1 sin 7 y + sin 3 y

1 2 sin ⁡ 7 y − 1 2 sin ⁡ 3 y \frac{1}{2}\sin7y-\frac{1}{2}\sin3y 2 1 sin 7 y − 2 1 sin 3 y

1 2 sin ⁡ 7 y − sin ⁡ 3 y \frac{1}{2}\sin7y-\sin3y 2 1 sin 7 y − sin 3 y

Find the exact value of the expression: sin ⁡ 165 ⋅ sin ⁡ 15 \sin165\cdot\sin15 sin 1 6 5 ⋅ sin 1 5

− 3 + 2 4 \frac{-\sqrt{3}+2}{4} 4 − 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 2

3 + 2 2 \frac{\sqrt{3}+2}{2} 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 2

3 − 2 2 \frac{\sqrt{3}-2}{2} 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 2

− 3 − 2 4 \frac{-\sqrt{3}-2}{4} 4 − 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 2

Find the exact value of the expression: 4 3 [ sin ⁡ 255 + sin ⁡ 15 ] \frac{4}{3}\left[\sin255+\sin15\right] 3 4 [ sin 2 5 5 + sin 1 5 ]

− 2 2 3 -\frac{2\sqrt{2}}{3} − 3 2 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

− 2 3 2 \frac{-2\sqrt{3}}{2} 2 − 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 2 3 \frac{2\sqrt{2}}{3} 3 2 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Rewrite the expression as a product: sin ⁡ 4 α ⋅ sin ⁡ 8 α \sin4\alpha\cdot\sin8\alpha sin 4 α ⋅ sin 8 α

2 sin ⁡ 6 α ⋅ cos ⁡ 2 α 2\sin6\alpha\cdot\cos2\alpha 2 sin 6 α ⋅ cos 2 α

2 cos ⁡ 6 α sin ⁡ 2 α 2\cos6\alpha\sin2\alpha 2 cos 6 α sin 2 α

2 cos ⁡ 2 α ⋅ sin ⁡ 6 α 2\cos2\alpha\cdot\sin6\alpha 2 cos 2 α ⋅ sin 6 α

2 sin ⁡ 2 α ⋅ sin ⁡ 6 α 2\sin2\alpha\cdot\sin6\alpha 2 sin 2 α ⋅ sin 6 α

sin ⁡ 5 B sin ⁡ B \sin5B\sin B sin 5 B sin B

cos ⁡ 4 B − cos ⁡ 6 B 2 \frac{\cos4B-\cos6B}{2} 2 cos 4 B − cos 6 B

sin ⁡ 4 B + cos ⁡ 6 B 2 \frac{\sin4B+\cos6B}{2} 2 sin 4 B + cos 6 B

sin ⁡ 6 B + sin ⁡ 4 B 2 \frac{\sin6B+\sin4B}{2} 2 sin 6 B + sin 4 B

cos ⁡ 4 B − sin ⁡ 6 B 2 \frac{\cos4B-\sin6B}{2} 2 cos 4 B − sin 6 B

cos ⁡ 4 B sin ⁡ B \cos4B\sin B cos 4 B sin B

sin ⁡ 5 B − sin ⁡ 3 B 2 \frac{\sin5B-\sin3B}{2} 2 sin 5 B − sin 3 B

sin ⁡ 5 B + cos ⁡ 3 B 2 \frac{\sin5B+\cos3B}{2} 2 sin 5 B + cos 3 B

cos ⁡ 5 B + cos ⁡ 3 B 2 \frac{\cos5B+\cos3B}{2} 2 cos 5 B + cos 3 B

cos ⁡ 5 B + sin ⁡ 3 B 2 \frac{\cos5B+\sin3B}{2} 2 cos 5 B + sin 3 B

cos ⁡ 57 ° sin ⁡ 55 ° \cos57\degree\sin55\degree cos 5 7 ° sin 5 5 °

sin ⁡ 112 ° − sin ⁡ 2 ° 2 \frac{\sin112\degree-\sin2\degree}{2} 2 sin 1 1 2 ° − sin 2 °

cos ⁡ 112 ° − cos ⁡ 2 ° 2 \frac{\cos112\degree-\cos2\degree}{2} 2 cos 1 1 2 ° − cos 2 °

sin ⁡ 2 ° + sin ⁡ 112 ° 2 \frac{\sin2\degree+\sin112\degree}{2} 2 sin 2 ° + sin 1 1 2 °

sin ⁡ 112 ° − cos ⁡ 2 ° 2 \frac{\sin112\degree-\cos\ 2\degree}{2} 2 sin 1 1 2 ° − cos 2 °

cos ⁡ 5 A − cos ⁡ A \cos5A-\cos A cos 5 A − cos A

− 2 sin ⁡ 3 A sin ⁡ 2 A -2\sin3A\sin2A − 2 sin 3 A sin 2 A

− 2 cos ⁡ 3 A cos ⁡ 2 A -2\cos3A\cos2A − 2 cos 3 A cos 2 A

− 2 sin ⁡ 3 A cos ⁡ 2 A -2\sin3A\cos2A − 2 sin 3 A cos 2 A

2 sin ⁡ 2 A cos ⁡ 3 A 2\sin2A\cos3A 2 sin 2 A cos 3 A

cos ⁡ 129 ° + cos ⁡ 45 ° \cos129\degree+\cos45\degree cos 1 2 9 ° + cos 4 5 °

2 cos ⁡ 87 ° cos ⁡ 42 ° 2\cos87\degree\cos42\degree 2 cos 8 7 ° cos 4 2 °

− 2 cos ⁡ 87 ° cos ⁡ 42 ° -2\cos87\degree\cos42\degree − 2 cos 8 7 ° cos 4 2 °

− 2 sin ⁡ 87 ° sin ⁡ 42 ° -2\sin87\degree\sin42\degree − 2 sin 8 7 ° sin 4 2 °

− 2 sin ⁡ 87 ° cos ⁡ 42 ° -2\sin87\degree\cos42\degree − 2 sin 8 7 ° cos 4 2 °

− 4 ( sin ⁡ 89 ° − sin ⁡ 167 ° ) -4\left(\sin89\degree-\sin167\degree\right) − 4 ( sin 8 9 ° − sin 1 6 7 ° )

8 cos ⁡ 128 ° sin ⁡ 39 ° 8\cos128\degree\sin39\degree 8 cos 1 2 8 ° sin 3 9 °

− 8 cos ⁡ 128 ° sin ⁡ 39 ° -8\cos128\degree\sin39\degree − 8 cos 1 2 8 ° sin 3 9 °

8 sin ⁡ 128 ° cos ⁡ 39 ° 8\sin128\degree\cos39\degree 8 sin 1 2 8 ° cos 3 9 °

− 8 sin ⁡ 39 ° sin ⁡ 128 ° -8\sin39\degree\sin128\degree − 8 sin 3 9 ° sin 1 2 8 °

sin ⁡ 16 θ + sin ⁡ 4 θ \sin16\theta+\sin4\theta sin 1 6 θ + sin 4 θ

2 sin ⁡ 10 θ cos ⁡ 6 θ 2\sin10\theta\cos6\theta 2 sin 1 0 θ cos 6 θ

− 2 cos ⁡ 10 θ cos ⁡ 6 θ -2\cos10\theta\cos6\theta − 2 cos 1 0 θ cos 6 θ

− 2 sin ⁡ 10 θ cos ⁡ 6 θ -2\sin10\theta\cos6\theta − 2 sin 1 0 θ cos 6 θ

− 2 sin ⁡ 10 θ sin ⁡ 6 θ -2\sin10\theta\sin6\theta − 2 sin 1 0 θ sin 6 θ

cos ⁡ 7 θ + cos ⁡ 13 θ \cos7\theta+\cos13\theta cos 7 θ + cos 1 3 θ

2 cos ⁡ 10 θ cos ⁡ 3 θ 2\cos10\theta\cos3\theta 2 cos 1 0 θ cos 3 θ

− 2 sin ⁡ 3 θ cos ⁡ 10 θ -2\sin3\theta\cos10\theta − 2 sin 3 θ cos 1 0 θ

− 2 cos ⁡ 3 θ cos ⁡ 10 θ -2\cos3\theta\cos10\theta − 2 cos 3 θ cos 1 0 θ

− 2 cos ⁡ 3 θ sin ⁡ 10 θ -2\cos3\theta\sin10\theta − 2 cos 3 θ sin 1 0 θ

− 5 cos ⁡ 3 θ + 5 cos ⁡ 7 θ -5\ \cos3\theta+5\cos7\theta − 5 cos 3 θ + 5 cos 7 θ

− 10 sin ⁡ 5 θ sin ⁡ 2 θ -10\sin5\theta\sin2\theta − 1 0 sin 5 θ sin 2 θ

10 sin ⁡ 5 θ cos ⁡ 2 θ 10\sin5\theta\cos2\theta 1 0 sin 5 θ cos 2 θ

− 10 sin ⁡ 2 θ cos ⁡ 5 θ -10\sin2\theta\cos5\theta − 1 0 sin 2 θ cos 5 θ

10 cos ⁡ 5 θ sin ⁡ 2 θ 10\cos5\theta\sin2\theta 1 0 cos 5 θ sin 2 θ

Product-to-Sum, Sum-to-Product Formula Fun

Authored by Paul Morris

Mathematics

8th - 12th Grade

CCSS covered

Used 139+ times

Product-to-Sum, Sum-to-Product Formula Fun

AI Actions

Add similar questions

Adjust reading levels

Convert to real-world scenario

Translate activity

More...

Content View

Student View

15 questions

Show all answers

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Rewrite the expression as a sum or difference: $\cos2y\ \cdot\sin\ 5y$

$\frac{1}{2}\sin7y+\frac{1}{2}\sin3y$

$\frac{1}{2}\sin7y+\sin3y$

$\frac{1}{2}\sin7y-\frac{1}{2}\sin3y$

$\frac{1}{2}\sin7y-\sin3y$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the exact value of the expression: $\sin165\cdot\sin15$

$\frac{\sqrt{3}+2}{2}$

$\frac{-\sqrt{3}+2}{4}$

$\frac{\sqrt{3}-2}{2}$

$\frac{-\sqrt{3}-2}{4}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the exact value of the expression: $\frac{4}{3}\left[\sin255+\sin15\right]$

$\frac{-2\sqrt{3}}{2}$

$\frac{2}{3}$

$\frac{2\sqrt{2}}{3}$

$-\frac{2\sqrt{2}}{3}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Rewrite the expression as a product: $\sin4\alpha\cdot\sin8\alpha$

$2\cos6\alpha\sin2\alpha$

$2\cos2\alpha\cdot\sin6\alpha$

$2\sin6\alpha\cdot\cos2\alpha$

$2\sin2\alpha\cdot\sin6\alpha$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Rewrite the expression in terms with no power greater than 1: $\cos^2x\cdot\csc x-\csc x$

$\frac{-\csc x+\csc x\cos2x}{2}$

$\csc x\sin^2x$

$\frac{\csc x-\csc x\cos2x}{2}$

$\frac{\cos2x-\csc x}{4}$

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSA.APR.D.6

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Rewrite the expression in terms with no power greater than 1: $\sin^2\theta\cdot\cos^2\theta$

$\frac{1}{8}-\frac{1}{8}\cos4\theta$

$1-\cos4\theta$

$\cos4\theta-1$

$\frac{-1}{8}+\frac{1}{8}\cos4\theta$

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\sin5B\sin B$

$\frac{\cos4B-\cos6B}{2}$

$\frac{\sin4B+\cos6B}{2}$

$\frac{\sin6B+\sin4B}{2}$

$\frac{\cos4B-\sin6B}{2}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\cos4B\sin B$

$\frac{\sin5B+\cos3B}{2}$

$\frac{\cos5B+\cos3B}{2}$

$\frac{\cos5B+\sin3B}{2}$

$\frac{\sin5B-\sin3B}{2}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\cos57\degree\sin55\degree$

$\frac{\cos112\degree-\cos2\degree}{2}$

$\frac{\sin112\degree-\sin2\degree}{2}$

$\frac{\sin2\degree+\sin112\degree}{2}$

$\frac{\sin112\degree-\cos\ 2\degree}{2}$

Tags

CCSS.HSF.TF.C.9

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\cos5A-\cos A$

$-2\cos3A\cos2A$

$-2\sin3A\sin2A$

$-2\sin3A\cos2A$

$2\sin2A\cos3A$

Tags

CCSS.HSF.TF.C.9

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

15 questions

Conocimientos Previos

Quiz

•

5th - 10th Grade

18 questions

Funciones Trigonometricas

Quiz

•

12th Grade

15 questions

Graphs of Trigonometric Functions 1

Quiz

•

10th Grade - Professi...

10 questions

2o Concurso de Matemáticas para 3er grado A4

Quiz

•

9th Grade

20 questions

Math 10C Labelling Right Triangles

Quiz

•

8th - 11th Grade

15 questions

Trigonometric Ratios

Quiz

•

7th - 9th Grade

20 questions

Trygonometria - kąty ostre

Quiz

•

9th - 10th Grade

12 questions

Integrale

Quiz

•

12th Grade

Popular Resources on Wayground

20 questions

"What is the question asking??" Grades 3-5

Quiz

•

1st - 5th Grade

20 questions

“What is the question asking??” Grades 6-8

Quiz

•

6th - 8th Grade

10 questions

Fire Safety Quiz

Quiz

•

12th Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

34 questions

STAAR Review 6th - 8th grade Reading Part 1

Quiz

•

6th - 8th Grade

20 questions

“What is the question asking??” English I-II

Quiz

•

9th - 12th Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

47 questions

8th Grade Reading STAAR Ultimate Review!

Quiz

•

8th Grade

Discover more resources for Mathematics

15 questions

Pythagorean Theorem Word Problems Quizizz

Quiz

•

8th Grade

20 questions

Graphing Inequalities on a Number Line

Quiz

•

6th - 9th Grade

20 questions

Scatter Plots and Line of Best Fit

Quiz

•

8th Grade

20 questions

Pythagorean Theorem Review

Quiz

•

8th Grade

46 questions

Linear and Exponential Function Key Features

Quiz

•

9th Grade

18 questions

CHS PSAT Prep

Quiz

•

9th Grade

21 questions

Factoring Trinomials (a=1)

Quiz

•

9th Grade

15 questions

Combine Like Terms and Distributive Property

Quiz

•

8th - 9th Grade

Product-to-Sum, Sum-to-Product Formula Fun

Rewrite the expression as a sum or difference: cos⁡2y ⋅sin⁡ 5y\cos2y\ \cdot\sin\ 5ycos2y ⋅sin 5y

Find the exact value of the expression: sin⁡165⋅sin⁡15\sin165\cdot\sin15sin165⋅sin15

Find the exact value of the expression: 43[sin⁡255+sin⁡15]\frac{4}{3}\left[\sin255+\sin15\right]34​[sin255+sin15]

Rewrite the expression as a product: sin⁡4α⋅sin⁡8α\sin4\alpha\cdot\sin8\alphasin4α⋅sin8α

Rewrite the expression in terms with no power greater than 1: cos⁡2x⋅csc⁡x−csc⁡x\cos^2x\cdot\csc x-\csc xcos2x⋅cscx−cscx

Rewrite the expression in terms with no power greater than 1: sin⁡2θ⋅cos⁡2θ\sin^2\theta\cdot\cos^2\thetasin2θ⋅cos2θ

sin⁡5Bsin⁡B\sin5B\sin Bsin5BsinB

cos⁡4Bsin⁡B\cos4B\sin Bcos4BsinB

cos⁡57°sin⁡55°\cos57\degree\sin55\degreecos57°sin55°

cos⁡5A−cos⁡A\cos5A-\cos Acos5A−cosA

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Rewrite the expression as a sum or difference: $\cos2y\ \cdot\sin\ 5y$

Find the exact value of the expression: $\sin165\cdot\sin15$

Find the exact value of the expression: $\frac{4}{3}\left[\sin255+\sin15\right]$

Rewrite the expression as a product: $\sin4\alpha\cdot\sin8\alpha$

Rewrite the expression in terms with no power greater than 1: $\cos^2x\cdot\csc x-\csc x$

Rewrite the expression in terms with no power greater than 1: $\sin^2\theta\cdot\cos^2\theta$

$\sin5B\sin B$

$\cos4B\sin B$

$\cos57\degree\sin55\degree$

$\cos5A-\cos A$