Question

Which two angles satisfy the equation

sin(3x + 2) = cos(x + 8)?
F, 11°, 79°
G, 20°, 70°
H, 44°, 46°
J, 62°, 28°

Answer 1

J, 62°, 28°

Explanation:

Since the principles of sine and cosine are based upon right triangles, the two angles have to be complementary, adding up to 90. Thereby, in your equation, (3x+2) + (x+8) = 90. Combining like terms gives you:

4x + 10 = 90 subtract 10 from both sides

- 10 -10

4x = 80 divide both sides by 4

4 4

x = 20 plug that back into both angles

3x+2 = 3(20) + 2 = 62°

x+8 = 20+8 = 28°

Answer is J 62°, 28°

Answer 2

Explanation:

Checking Option F:

`sin\left(3x+2\right)\:=\:cos\left(x+8\right)`

Checking x = 11° in above equation

`sin\left(3\left(11\right)+2\right)=cos\left(11+\:8\right)`

`\sin \left(35\right)=\cos \left(11^(\circ \:)+8\right)`

`\sin \left(35^(\circ \:)\right)=\cos \left(19^(\circ \:)\right)`

`\mathrm{The\:sides\:are\:not\:equal}`

`False`

Checking x = 79° in above equation

`sin\left(3\left(79\right)+2\right)\:=\:cos\left(79+8\right)`

`\sin \left(239\right)=\cos \left(79^(\circ \:)+8\right)`

`\sin \left(239\right)=\cos \left(79^(\circ \:)+8\right)`

`\mathrm{The\:sides\:are\:not\:equal}`

`False`

Checking Option G:

Checking x = 20° in above equation

`sin\left(3\left(20\right)+2\right)\:=\:cos\left(20+8\right)`

`\sin \:\left(62\right)=\cos \:\left(28\right)`

The sides are not equal

False

Checking x = 70° in above equation

`sin\left(3\left(70\right)+2\right)\:=\:cos\left(70+8\right)`

`\sin \left(212\right)=\cos \left(70^(\circ \:)+8\right)`

The sides are not equal

False

Checking Option H:

Checking x = 44° in above equation

`sin\left(3\left(44\right)+2\right)\:=\:cos\left(44+8\right)`

`\sin \left(134\right)=\cos \left(44^(\circ \:)+8\right)`

The sides are not equal

False

Checking x = 46° in above equation

`sin\left(3\left(46\right)+2\right)\:=\:cos\left(46+8\right)`

`\sin \left(140\right)=\cos \left(46^(\circ \:)+8\right)`

The sides are not equal

False

Checking Option J:

Checking x = 62° in above equation

`sin\left(3\left(62\right)+2\right)\:=\:cos\left(62+8\right)`

`\sin \left(188\right)=\cos \left(62^(\circ \:)+8\right)`

The sides are not equal

False

Checking x = 28° in above equation

`sin\left(3\left(28\right)+2\right)\:=\:cos\left(28+8\right)`

`\sin \left(86\right)=\cos \left(28^(\circ \:)+8\right)`

The sides are not equal

False

Therefore, NO TWO angles satisfy the equation

sin(3x + 2) = cos(x + 8).