€

tan x =33

, x =π6

,π3

,2π3

,5π6

,7π6

,4π3

Pre calculus Problem of the DayHomework: p. 619 1-57 eoo

Use substitution to determine which of the given x values are solutions to the equation.

€

x =π6

,7π6

Solving Trigonometric Equations, Finding all Solutions

€

tan x =33

€

x =π6

+ 2πn or x =7π6

+ 2πn

Where n is any integer.

An equivalent answer would be

€

x =π6

+πn

€

2cos2 x −1 = 0

€

Isolate a function to solve a trigonometric equation.

€

2cos2 x =1

€

cos2 x =12

€

cos x = ±12

= ±22

€

x =π4

+ 2πn,3π4

+ 2πn,5π4

+ 2πn,7π4

+ 2πn

Solve a trigonometric equation by factoring.

€

tan x sin x = sin x

€

tan x sin x −sin x = 0

€

sin x tan x −1( ) = 0

€

tan x −1 = 0 sin x = 0

€

x =π4

+ 2πn x= 0 + 2πn

=5π4

+ 2πn = π + 2πn

€

sin 4x = −32

Solving a trigonmetric equation over an interval.

Find all solutions on the interval [ 0, 2¶ ).

€

sinA = −32

€

A =4π3

+ 2πn or5π3

+ 2πn

€

4x =4π3

+ 2πn or5π3

+ 2πn

€

x =4π12

+2πn

4or

5π12

+2πn

4

€

x =π3

,5π6

,4π3

,11π

6or

5π12

,11π12

,17π12

,23π12

Pre calculus Problem of the DayHomework: p. 619 63 - 83 odds, 85-109 eoo

Solve the following over the interval [ 0, 2¶).

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tan 3x = −33