trig handout topic 12 solutions

7/30/2019 Trig Handout Topic 12 Solutions

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TOPIC 12 SOLVING TRIG EQUATIONS II (USING IDENTITIES)

In this final topic well review solving Trigonometric Equations (algebraically and graphically), and explore some

challenging equations that require the use of identities to simplify.

Solve algebraically:

Solve graphically on

Explore Consider the solution to the equation ;

Solve graphically on

Solve graphically by graphing in degree mode and finding the zeroes.

(Convert all answers to radians)

Solve algebraically by using the identity .

State the solutions on the interval

Provide a general solution.

GENERAL SOLUTION:

x90 180 270 360

y

- 2

- 1

1

2

x- 180 - 90 90 180

y

- 2

- 1

1

2


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Along with FACTORING, we can use the quotient, reciprocal, Pythagorean, addition/subtraction and double-

angle identities provided on the formula sheet to help algebraically solve trig equations.

We must watch for non-permissible values when our

equations involve quotient terms.

Connect

We can verify an equations solutions graphically. Although we can graph in radian mode (and experiment

with the window to see points of intersect / zeros), it is often easier to graph in degree mode and convert

solutions to radians. (if necessary)

Solve on

Consider the equation

If we scale carefully (in this case ) we can

see the solutions are , and

But if we use the zero or

intersect function on our

graphing calc we get the

radian answers in irrational

decimal form, not as exact

values in terms of

First solution

is

But calc gives the decimal

version of !

Again with a scale of we see the solutions are

, and . (same once converted!)

And if we use the

zero or intersect

function on our

graphing calc we ge

the degree answers

which are easily

convertible!

First solution

is

Which we can easily

convert from !

Solutions are , and

But non-permissible values are

then every (at vertical asymptotes)

(on )

Algebraic approach to determining

non-permissible values:

Non-permissible values where

(top/bottom of unit

circle), that is,

Graph in radian mode: Graph in degree mode:


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1. Consider the equation on(a) Solve algebraically by factoring and referring to the unit circle.

(b) State the solutions on

(c) Verify your solutions graphically. Provide a sketch here, and label all solutions.

2. Algebraically solve the equation . (on )

Practice

x90 180 270 360

y

- 2

- 1

1

2


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3. Algebraically solve the equation on , and provide ageneral solution.

4. Algebraically solve the following equations on :(a) (b)

(b) (c)


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5.

6.

7.

trig handout topic 12 solutions

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