Given the Equation, , There Are Several Solutions (Several Angles with a Sine Value of )

MA 15400 Lesson 12 Section 7.2

Trigonometric Equations

Given the equation,, there are several solutions (several angles with a sine value of ½ ). When solving such an equation you may be asked to only find solutions in a given interval. If asked to find all real solutions, you will have to write an expression to represent such solutions. (This is the 'new part' of today's lesson.) To represent these infinite solutions, we will use n to represent an arbitrary integer.

Find all solutions of the equation.

a) Interval [0, 2p)

b) All Real Numbers

a) (Q I and IV)

b) The period of the cosine is 2π. b) The period of the

Any coterminal angles would also tangent is π.

be solutions.

n = ...-2, -1, 0, 1, 2, ...

*

Find all the solutions of the equation. [You are to solve for the variable.]

(Isolate the function first.)

(Take positive/negative square roots)

(Always give simplest answer)

2