Download precalc ch5sec5

PreCalculus Warm-up 05/21/2012
1. What are the solutions for the following
trigonometric equation on the interval [0, 2π):
cos2x + cosx = 6 ?
2. Find the exact value of tan(105o).
sin(    )
3. Verify that: cos  cos   tan   tan  .
4. Write cos25ocos15o – sin25osin15o as the trig
function of one angle.
5. Describe the general solution(s) for the
3

cos
x


following: 
4
3


  cos x 
4



  0.

5.4 Double and Half Angle Formulas
p.471 in your book- Double Angle Formulas:
Example: Suppose the tanx = (4/5), find the sin2x,
cos2x, and the tan2x.
Example: If the cotu = -6, find the tan2u, given that
3π/2 < u < 2π.
Example: Solve the equation 2cosx + 2sin2x = 0 on
the interval from [0,2π).
p.414 in your book- Half Angle Forumlas**
or
or
**Whether or not you use the + or the – depends on
where the angle is located!**
Example: Find the exact value of sin105o.
**105o is half of 210o.
Example: Given that tanθ = 12/5, find sin(θ/2) ,
csc(θ/2) , cos(θ/2) , sec(θ/2) , and cot(θ/2).
Example: Find the zeros of the function
f(x) = sin(x/2) + cosx – 1 on the interval [0,2π).
Assignments: text p.475 #1,5,7,9,11,12,23,24,3126,43,45,51,