Solving Trigonometric Equation Pre Calculus 5 3 To

• To solve trigonometric equations, we must solve for all values of the

Trigonometric Equations sin x = x= π 6 is a trigonometric equation. is one

Find the general solution for the equation sec = 2. From cos = 1

Solve the equation Trigonometric Equations

Solve the equation in the interval [0, 2π) Trigonometric Equations

Solve the equation in the interval (6π, 8π) Trigonometric Equations

Solve the equation in the interval (4π, 6π) Trigonometric Equations

Find all solutions of the equation Trigonometric Equations

• Homework • page 364 - 365 3, 5, 11, 15 21, 25,

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Solving Trigonometric Equation Pre. Calculus 5 -3

• To solve trigonometric equations, we must solve for all values of the variable that make the equation true. Trigonometric Equations

Trigonometric Equations sin x = x= π 6 is a trigonometric equation. is one of infinitely many solutions of y = sin x. y -19π 6 -11π 6 -3π -7π 6 1 -2π -π -1 5π 6 13π 6 π 2π 17π 6 3π 25π 6 x y= 4π All the solutions for x can be expressed in the form of a general solution. x= π 6+ 2 k π and x = 5π 6+ 2 k π (k = 0, ± 1, ± 2, ± 3, ).

Find the general solution for the equation sec = 2. From cos = 1 , it follows that cos = sec All values of for which cos = are solutions of the equation. π Two solutions are = ±. 3 π that are coterminal All angles 3 with ± are also solutions and can be expressed by adding integer multiples of 2π. The general solution can be written as cos( π3+ 2 kπ) = P y 1 x Q -π cos( 3+ 2 kπ) = = ± π3+ 2 kπ. 4

Trigonometric Equations