Double Angle Trigonometric Identities

Hello Pre-Calculus 40S class of slot C! It's Julie Umali !
Today in class we learned new identities! Double Angle Trig Identities to be exact. 
These identities deal with trig functions that have angles that are doubled.


So here are your new identities:
sin(2θ) = 2•sinθ•cosθ
cos(2θ) = cos²θ − sin²θ or 1-2sin²θ or 2cos²θ − 1
tan(2θ) = 2tanθ/(1-tan²θ) or sin2θ/cos2θ


Don't forget your inverse trig functions!
csc(2θ) = 1/(sin(2θ))
sec(2θ) = 1/(cos(2θ))
cot(2θ) = 1/(tan(2θ)) or cos(2θ)/sin(2θ)


Example:
1) Problem: If the sinθ = (3/8) and 0≤θ≤π/2 , then what is sin2θ?
(Use the figure below.)

Solution: From the diagram, we see that cosθ= √(55)/8. Use the double angle identity for sin:

sin 2θ = 2(sinθ)(cosθ)

Plug in the values you know:

sin 2θ = 2•(3/8)•(√(55)/8)

Perform the indicated multiplications and your answer will be:

sin 2θ = (3√(55))/32

Homework: Exercise 18, Questions 4-10, 13-18

Double Angle Identities Worksheet.