8-4 Guide and Intervention Trigonometry Trigonometric Ratios The ratio of the lengths of two sides of a right triangle is called a trigonometric ratio. The three most common ratios are sine, cosine, and tangent, which are abbreviated and respectively. sin, cos, tan, sin = cos = tan = R R R = = = Example: Find sin cos and tan Express each ratio as a fraction and a A, A, A. decimal to the nearest hundredth. sin = cos = tan = A A A = = = = = = 0.38 0.92 0.42 ≈ ≈ ≈ Exercises Find sin cos tan sin cos and tan Express each ratio as a fraction and as a decimal to the nearest J, J, J, L, L, L. hundredth if necessary. 1. 2. 3. 8-4 Study Guide and Intervention (continued) Trigonometry Use Inverse Trigonometric Ratios You can use a calculator and the sine, cosine, or tangent to find the measure of the angle, called the inverse of the trigonometric ratio. Example: Use a calculator to find the measure of to the nearest tenth. The measures given are those of the leg opposite and the ∠T hypotenuse, so write an equation using the sine ratio. sin = sin = T T If sin = , then = T m∠T. Use a calculator. So, 58.5. m∠T ≈ Exercises Use a calculator to find the measure of to the nearest tenth. 1. 2. 3.
8-4 Guide and Intervention Trigonometry Trigonometric Ratios The ratio of the lengths of two sides of a right triangle is called a trigonometric ratio. The three most common ratios are sine, cosine, and tangent, which are abbreviated sin, cos, and tan, respectively. sin R = cos R = tan R = = = = Example: Find sin A, cos A, and tan A. Express each ratio as a fraction and a decimal to the nearest hundredth. sin A = cos A = tan A = = = = = = = ≈ 0.38 ≈ 0.92 ≈ 0.42 Exercises Find sin J, cos J, tan J, sin L, cos L, and tan L. Express each ratio as a fraction and as a decimal to the nearest hundredth if necessary. 1. 2. 3. 8-4 Study Guide and Intervention (continued) Trigonometry Use Inverse Trigonometric Ratios You can use a calculator and the sine, cosine, or tangent to find the measure of the angle, called the inverse of the trigonometric ratio. Example: Use a calculator to find the measure of to the nearest tenth. The measures given are those of the leg opposite ∠T and the hypotenuse, so write an equation using the sine ratio. sin T = sin T = If sin T = , then = m∠T. Use a calculator. So, m∠T ≈ 58.5. Exercises Use a calculator to find the measure of to the nearest tenth. 1. 2. 3.