Chapter 5: Trigonometric Functions Lesson 7: General Solutions to Trigonometric Equations Mrs. Parziale

Vocabulary General Solutions – a basic way to write an equation for all possible values (infinitely many) without listing all values.

Example 1: Solve for all : Use the calculator. Graph y = sin(x) and y = 0.4199. Set your window to have x-max of 4 How many solutions. How would you write them all? Find two key ones – How often do they repeat?  

Example 1: Solve for all : General solution are _____________________ or ____________________________

Finding the Other Angle Measure For TRIG(x) = A (i.e. sin(x) = .4199) Look at A. Determine if it is positive or negative and write down which quadrants your answers will be in. Take the INVERSETRIG (|A|) and write it down as the ref angle. Then, calculate the other angle as follows: Quad II Quad 1Quad I Quad III Quad IV Write this down

Example 2: Solve for all in radians: General solutions are _____________________ or ____________________________

Example 3: a) Find all values for (x) in radians:

Example 3, cont. b) Find all values for  in radians: Use calculator and write the general solution. Remember, the period of tangent is .

Example 3, cont. c) Find all values for  in radians: Use the unit circle and write the general solution.

Example 4: Find all values for (x) in radians:

Closure What is a general solution? What is added to either a sin or cos function in the general solution? What is added to the tan function in the general solution? Solve the following: