Solving Trigonometric Equations Using Identities Multiple Ang This trigonometry video tutorial shows you how to solve trigonometric equations using identities with multiple angles, by factoring, and by finding the gener. Solving trigonometric equations with multiple angles. sometimes it is not possible to solve a trigonometric equation with identities that have a multiple angle, such as \(\sin(2x)\) or \(\cos(3x)\). when confronted with these equations, recall that \(y=\sin(2x)\) is a horizontal compression by a factor of 2 of the function \(y=\sin x\).
Trigonometric Equations Using Identities Multiple Angles By F 1 tan2θ = 1 (sinθ cosθ)2 rewrite left side = (cosθ cosθ)2 (sinθ cosθ)2 write both terms with the common denominator = cos2θ sin2θ cos2θ = 1 cos2θ = sec2θ. recall that we determined which trigonometric functions are odd and which are even. the next set of fundamental identities is the set of even odd identities. In this first section, we will work with the fundamental identities: the pythagorean identities, the even odd identities, the reciprocal identities, and the quotient identities. we will begin with the pythagorean identities, which are equations involving trigonometric functions based on the properties of a right triangle. Solving trigonometric equations with multiple angles. sometimes it is not possible to solve a trigonometric equation with identities that have a multiple angle, such as sin(2x)sin(2x) or cos(3x).cos(3x). when confronted with these equations, recall that y=sin(2x)y=sin(2x) is a horizontal compression by a factor of 2 of the function y=sinx.y=sinx. Using the zero product theorem, we know that this product will be equal to zero if either factor is equal to zero, allowing us to break this equation into two cases: sin( t ) 0 or 2 sin( t ) 1 0. we can solve each of these equations independently sin( t ) 0 from our knowledge of special angles. t = 0 or t = π.
How To Solve Trigonometric Equations With Multiple Angles Solving trigonometric equations with multiple angles. sometimes it is not possible to solve a trigonometric equation with identities that have a multiple angle, such as sin(2x)sin(2x) or cos(3x).cos(3x). when confronted with these equations, recall that y=sin(2x)y=sin(2x) is a horizontal compression by a factor of 2 of the function y=sinx.y=sinx. Using the zero product theorem, we know that this product will be equal to zero if either factor is equal to zero, allowing us to break this equation into two cases: sin( t ) 0 or 2 sin( t ) 1 0. we can solve each of these equations independently sin( t ) 0 from our knowledge of special angles. t = 0 or t = π. Solve a trigonometric equation by factoring. find all solutions of sin x tan x sin x = 0. solution. begin by factoring out the common factor, sin x. sin x tan x sin x = 0. sin x (tan x 1) = 0. apply the zero product property and set each factor equal to zero and solve. sin x = 0. tan x 1 = 0. In this first section, we will work with the fundamental identities: the pythagorean identities, the even odd identities, the reciprocal identities, and the quotient identities. we will begin with the pythagorean identities (see (figure)), which are equations involving trigonometric functions based on the properties of a right triangle.
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