Download Trigonometric Equations

Section 5.5: Solving Trig. Equations
RECALL: A trig. identity is an equation which is ALWAYS true: sin2 θ + cos2 θ = 1
Now you’ll be solving conditional equations which are only true for certain values.
ex) Use the unit circle to determine what radian angle measures between 0 to 2 π
satisfy this equation:
sinθ = cos θ
Solution for [0,2π] interval.
θ = ____________________
Are these the ONLY solutions?
What if you were asked to describe a general solution?
ex) Solve the equation sec θ = −2 for θ values in the interval [0,2π] .
ex) Find the general solution to the equation cot2 (θ) − 3 = 0 .
ex) Solve the equation (cos θ + 1)(2sinθ − 1) = 0 for values in the interval [0,2π] .
ex) Solve the equation sin2 θ − cos θ + 1 = 0 for values in the interval [0,2π] .
Multiples in the Argument
ex) Solve the equation 2sin(3θ ) = 1 for values in the interval [0,2π]
ex) Solve the equation tan( 23 θ ) =−1 for values in the interval [0,2π]