Double Angle Formulas

Definition: Double angle formulas are trigonometric identities involving functions of double angles (sin 2x, cos 2x and tan 2x). These formulas are helpful when simplifying trigonometric expressions.

There are double angle formulas for sine, cosine, and tangent:

Example: Given cos x = 4/5, find sin 2x when 270 < x < 360

Solution: 

Step 1: Determine the best formula to use.

We need to find sin2x, so can use the formula sin 2x = 2 sin x cos x.

Step 2: Find the value of sin x.

In order to use this formula, we’ll need to find the value of sin x. We already know cos x = -4/5, so drawing a right triangle or using the Pythagorean identity will be helpful hereWe can see that sin x = 3/5, but because the problem stated 270 < x < 360, this tells us x is in Quadrant IV (where sin is negative), so sin x = -3/5.

Step 3: Plug cos x and sin x into the formula and simplify.

sin 2x = 2 sin x cos x

sin 2x= 2(-3/5)(4/5) = -24/25.

sin 2x = -24/25

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