Trigonometry – Sine Double Angle Identity

By | September 20, 2016

Sine Double Angle Identity

In this tutorial students learn how to verify a trigonometric equation.  The students will learn to use trigonometric identities like the Double Angle Identity and the Pythagorean Identity.

Virginia Standards of Learning (SOL) T.5

Key Skills

Pythagorean Identities

sin²x + cos²x = 1

1 + cot²x = csc²x

tan²x + 1 = sec²x

Trigonometric Identities

1/cos(x) = sec(x)

1/sin(x) = csc(x)

tan(x) = sin(x)/cos(x)

1/tan(x) = cos(x)/sin(x)

1/tan(x) = cot(x)

Sine Double Angle Identity

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

Cosine Double Angle Identity

cos(2x) = cos²(x) - sin²(x)

Conjugate

A binomial where the second term is negated.

(x + 2) conjugate (x - 2)

(1 - cos x) conjugate (1 + cos x)

Difference of Perfect Squares

The subtraction of 2 perfect squares can be factored as you see below.

(a² - b²) = (a + b) (a - b)

More examples