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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,