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Solve the following trigonometric equations (state how many solutions as well as the val- ues). Give answers to 2 decimal places (for degrees) or as fractions of π for radians.
Created by T. Madas Created by T. Madas 9. sin 3cos 2sin 3 3 x x x π π + − + ≡ (**) 10. cos 3sin 2cos 3 3 x x x π π
Examples Example 1 Solve csc(x) + 6 = 1 — graphing technology. Solution 3 csc(x), where 0 < x < 27r, correct to two decimal places. Verify the solution using First, we identify any non-permissible values of x. Cosecant of x is undefined when x = n7r, n e Z.
This unit looks at the solution of trigonometric equations. In order to solve these equations we shall make extensive use of the graphs of the functions sine, cosine and tangent.
EQUATION SOLVING: Example 1: Find all possible values of T so that 2 1 cosT . Solution: Sn S T 2 3 , Sn S T 2 3 5 , where n is an integer. Solution Method #1 – Graphically: There are an infinite number of solutions which are represented by the value of intersection points of the cosine curve and the constant function 2 1 y. y cosx 2 For 0dTd2S
Trigonometry: Law of Sines, Law of Cosines, and Area of Triangles. Formulas, notes, examples, and practice test (with solutions) Topics include finding angles and sides, the “ambiguous case” of law of Sines, vectors, navigation, and more.
Example 1 Solve 2sin 2 (t) sin(t) 0 for all solutions with 0dt 2S. This equation kind of looks like a quadratic equation, but with sin(t) in place of an algebraic variable (we often call such an equation “quadratic in sine”). As with all quadratic equations, we can use factoring techniques or the quadratic formula. This
