Exploring the Double Angle Formula for Cosine

What theorem is used to confirm that triangle ABC is a right triangle?

• Law of cosines

• Law of sines

• Triangle inequality theorem

• Pythagorean theorem

Tags

CCSS.8.G.B.8

What is the cosine of angle ABC in triangle ABC?

• 3/5

• 4/5

• 5/3

• 5/4

Tags

CCSS.HSG.SRT.C.6

What is the sine of angle ABC in triangle ABC?

• 5/3

• 5/4

• 3/5

• 4/5

Tags

CCSS.HSG.SRT.C.6

What is the hypotenuse of triangle ABC?

• 5

• 3

• 4

• 6

What is the adjacent side length of angle ABC in triangle ABC?

• 3

• 4

• 5

• 6

Tags

CCSS.HSG.SRT.C.6

What is the opposite side length of angle ABC in triangle ABC?

• 4

• 3

• 6

• 5

Which trigonometric identity is used to find the cosine of 2 times an angle?

• tan(2x) = 2tan(x)/(1-tan^2(x))

• cos(2x) = 2cos^2(x) - 1

• sin(2x) = 2sin(x)cos(x)

• cos(2x) = cos^2(x) - sin^2(x)

Tags

CCSS.HSF.TF.C.9

What is the value of cos(2 times angle ABC)?

• 7/25

• 25/7

• -7/25

• -25/7

Tags

CCSS.HSF.TF.C.9

Why does the cosine of 2 times angle ABC result in a negative value?

• The angle is in the first quadrant where cosine is positive.

• The angle is in the fourth quadrant where cosine is negative.

• The angle is in the third quadrant where cosine is positive.

• The angle is in the second quadrant where cosine is negative.

Tags

CCSS.HSF.TF.A.4

What does the negative result of cos(2 times angle ABC) indicate about the angle's position?

• It is in a quadrant where cosine values are negative.

• It is in a quadrant where cosine values are positive.

• It indicates an error in calculation.

• It suggests the triangle is not a right triangle.

Tags

CCSS.HSF.TF.C.9