Double Angle Identities A

Front

Define Double Angle Identities.

Back

Double Angle Identities are trigonometric identities that express trigonometric functions of double angles (2x) in terms of functions of single angles (x).

Front

What is the Double Angle Identity for sine?

Back

sin(2x) = 2sin(x)cos(x)

Front

What is the Double Angle Identity for cosine?

Back

cos(2x) = cos²(x) - sin²(x) or cos(2x) = 2cos²(x) - 1 or cos(2x) = 1 - 2sin²(x) depending on the form used.

Front

What is the Double Angle Identity for tangent?

Back

tan(2x) = 2tan(x) / (1 - tan²(x))

Front

If sin(x) = 12/13, find sin(2x).

Back

sin(2x) = 2sin(x)cos(x) = 2(12/13)(5/13) = 120/169.

Front

If cos(x) = -4/5 in quadrant II, find csc(x).

Back

csc(x) = 1/sin(x) = 5/3.

Front

If cos(x) = -4/5, find sec(x).

Back

sec(x) = 1/cos(x) = -5/4.

Front

Using the fourth identity, find cos(120°).

Back

cos(120°) = 1 - 2sin²(60°).

Front

Using the third identity, find cos(40°).

Back

cos(40°) = 2cos²(20°) - 1.

Front

What is the relationship between sine and cosine in the context of double angle identities?

Back

Sine and cosine are related through the Pythagorean identity: sin²(x) + cos²(x) = 1, which is used in deriving double angle identities.