Solving Trigonometric Equation Pre Calculus 5 3 To

• Slides: 33

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

Solve the equation Trigonometric Equations

Trigonometric Equations

Solve the equation Trigonometric Equations

Trigonometric Equations

Trigonometric Equations

Solve the equation Trigonometric Equations

Solve the equation Trigonometric Equations

Solve the equation Trigonometric Equations

Trigonometric Equations

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

Trigonometric Equations

Solve the equation Trigonometric Equations

Trigonometric Equations

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

Trigonometric Equations

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

Trigonometric Equations

Trigonometric Equations

Solve the equation Trigonometric Equations

Trigonometric Equations

Trigonometric Equations

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

Trigonometric Equations

Find all solutions of the equation Trigonometric Equations

Trigonometric Equations

Trigonometric Equations

Solve the equation Trigonometric Equations

• Homework • page 364 - 365 3, 5, 11, 15 21, 25, 27, 29, 33, 35, 53, 55, 67 Trigonometric Equations