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Honors Physics Chapter 1 Trigonometry Review We will be working with the sine, cosine, and tangent functions in this course. These functions are defined for right triangles as follows: sin Opposite Hypotenuse hypotenuse cos adjacent hypotenuse opposite θ opposite tan adjacent adjacent These relationships can be remembered with the pneumonic device, soh cah toa. Examples Use the trigonometric functions to find the missing lengths for the following triangle. 1. x 5 30° Look at the triangle and identify which sides you have. The side with a value of 5 is opposite of the 30 degree angle. The side with the value of x is the hypotenuse. Now select the trigonometric function that relates the opposite side and the hypotenuse. sin Opposite Hypotenuse sin 30 5 Solve this equation for x. x x sin 30 5 5 x sin 30 x 10 1 Honors Physics Chapter 1 2. For this triangle the sides are the adjacent side and the hypotenuse. Therefore, we use the cosine function. 40° x 12 x 12 x 12 cos 40 x 9.19 cos 40 x 12 12×tan25°=x x=5.6 tan25°= 3. x 25° 12 This is how we use the trigonometric functions to find the length of the sides of a right triangle. We can also use it to find the angles in a triangle. Examples – Find the value for the angle, θ, in each of the following problems. 1. θ 12 Identify the sides that are known. In this problem we know the side that is opposite of θ and the hypotenuse. This means that we choose the sine function. 8 8 12 In order to solve this equation, we must use the inverse trigonometric functions. We take the inverse sine (sin-1) of both sides of the equation. sinθ= sin -1 (sinθ) =sin -1 ( 8 ) 12 θ = 42° 2 Honors Physics Chapter 1 3 θ 4 Find the value of θ and the length of the missing side of the triangle. 2. θ 8 2 Find the value of θ. 3. More Trig Review Problems θ 8.0 6.0 1. Solve for θ and missing side of triangle. 3 Honors Physics Chapter 1 y 12 20.0° 2. Solve for y and missing side of triangle. 50° 4.5 x 3. Solve for x. θ 3.1 4. 6.4 Solve for θ. 4 Honors Physics Chapter 1 14 θ 10 Solve for θ. 5. 60 z 5.0 6. Solve for z. 0.577 θ 1.0 Solve for θ. 7. 5