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**International Studies Charter School. Right Triangle Trigonometry**

Mrs. Rivas International Studies Charter School. Pre-Calculus Section 4.3 Right Triangle Trigonometry

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Geometry Review

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**Trigonometry Functions**

There are six trigonometry functions. Sine (sin), Cosine (cos), Tangent (tan), Secant (sec), Cosecant (csc), Cotangent (cot) Some people remember the first three trigonometry functions by: SOH CAH TOA

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**Trigonometry Functions**

𝑹𝒆𝒄𝒊𝒑𝒓𝒐𝒄𝒂𝒍𝒔 SOHCAHTOA 𝒄 𝒂 𝐬𝐢𝐧 𝜽= 𝒂 𝒄 𝐜𝐬𝐜 𝜽= 𝒄 𝒂 𝜽 𝒃 𝒄 = hypotenuse 𝐜𝐨𝐬 𝜽= 𝒃 𝒄 𝐬𝐞𝐜 𝜽= 𝒄 𝒃 𝒂 = opposite side 𝒃 = adjacent side 𝐜𝐨𝐭 𝜽= 𝒃 𝒂 𝐭𝐚𝐧 𝜽= 𝒂 𝒃

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**Trigonometry Functions**

Examples: What are the sine, cosine and tangent ratios for T.

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**Trigonometry Functions**

Examples: What are the secant, cosecant and cotangent ratios for T. 𝐜𝐬𝐜 𝑻= 𝒉𝒚𝒑𝒐𝒕𝒆𝒔𝒏𝒖𝒔𝒆 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝐬𝐞𝐜 𝑻= 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒉𝒚𝒑𝒐𝒕𝒆𝒔𝒏𝒖𝒔𝒆 𝐜𝐨𝐭 𝑻= 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕

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**Trigonometry Functions**

Examples: Find the value of 𝒙. Round to the nearest tenth. x 20 Sin 35º = 20 20 20 = x 11.47 = x 11.5 ≈ x

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**Right Triangle Trigonometry**

Mrs. Rivas International Studies Charter School. Pre-Calculus Section 4.3 Right Triangle Trigonometry Use right triangles to evaluate trigonometric functions

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**International Studies Charter School. Right Triangle Trigonometry**

Mrs. Rivas International Studies Charter School. Pre-Calculus Section 4.3 Right Triangle Trigonometry

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**International Studies Charter School. Right Triangle Trigonometry**

Mrs. Rivas International Studies Charter School. Pre-Calculus Section 4.3 Right Triangle Trigonometry

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**International Studies Charter School. Right Triangle Trigonometry**

Mrs. Rivas International Studies Charter School. Pre-Calculus Section 4.3 Right Triangle Trigonometry

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**International Studies Charter School. Right Triangle Trigonometry**

Mrs. Rivas International Studies Charter School. Pre-Calculus Section 4.3 Right Triangle Trigonometry Find function values for 𝟑𝟎° 𝝅 𝟔 , 𝟒𝟓° 𝝅 𝟒 , 𝟔𝟎° 𝝅 𝟑

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**International Studies Charter School. Right Triangle Trigonometry**

Mrs. Rivas International Studies Charter School. Pre-Calculus Section 4.3 Right Triangle Trigonometry

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**International Studies Charter School. Right Triangle Trigonometry**

Mrs. Rivas International Studies Charter School. Pre-Calculus Section 4.3 Right Triangle Trigonometry

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**International Studies Charter School. Right Triangle Trigonometry**

Mrs. Rivas International Studies Charter School. Pre-Calculus Section 4.3 Right Triangle Trigonometry

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**International Studies Charter School. Right Triangle Trigonometry**

Mrs. Rivas International Studies Charter School. Pre-Calculus Section 4.3 Right Triangle Trigonometry Use equal cofunctions of complements Two positive angles are complements if their sum is 90°or 𝝅 𝟐 . For example, angles of 70° and 20° are complements because 70°+20°=90°. In Section 4.2, we used the unit circle to establish fundamental trigonometric identities. Another relationship among trigonometric functions is based on angles that are complements. Refer to Figure Because the sum of the angles of any triangle is 180°, in a right triangle the sum of the acute angles is 90°. Thus, the acute angles are complements. If the degree measure of one acute angle is 𝜃, then the degree measure of the other acute angle is 90°−𝜃 . This angle is shown on the upper right in Figure 4.36.

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**International Studies Charter School. Right Triangle Trigonometry**

Mrs. Rivas International Studies Charter School. Pre-Calculus Section 4.3 Right Triangle Trigonometry Let’s use Figure 4.36 to compare sin 𝜃 and cos 𝜃 . Thus, sin 𝜃= cos 90°−𝜃 . If two angles are complements, the sine of one equals the cosine of the other. Because of this relationship, the sine and cosine are called cofunctions of each other. The name cosine is a shortened form of the phrase complement’s sine.

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**International Studies Charter School. Right Triangle Trigonometry**

Mrs. Rivas International Studies Charter School. Pre-Calculus Section 4.3 Right Triangle Trigonometry Any pair of trigonometric functions 𝑓 and 𝑔 for which 𝑓 𝜃 =𝑔(90°−𝜃) and 𝑔 𝜃 =𝑓(90°−𝜃) are called cofunctions. Using Figure 4.36, we can show that the tangent and cotangent are also cofunctions of each other. So are the secant and cosecant.

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**International Studies Charter School. Right Triangle Trigonometry**

Mrs. Rivas International Studies Charter School. Pre-Calculus Section 4.3 Right Triangle Trigonometry

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**International Studies Charter School. Right Triangle Trigonometry**

Mrs. Rivas International Studies Charter School. Pre-Calculus Section 4.3 Right Triangle Trigonometry Use right triangle trigonometry to solve applied problems. Many applications of right triangle trigonometry involve the angle made with an imaginary horizontal line. As shown in Figure 4.37, an angle formed by a horizontal line and the line of sight to an object that is above the horizontal line is called the angle of elevation. The angle formed by a horizontal line and the line of sight to an object that is below the horizontal line is called the angle of depression. Transits and sextants are instruments used to measure such angles.

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**International Studies Charter School. Right Triangle Trigonometry**

Mrs. Rivas International Studies Charter School. Pre-Calculus Section 4.3 Right Triangle Trigonometry Sighting the top of a building, a surveyor measured the angle of elevation to be 22°. The transit is 5 feet above the ground and 300 feet from the building. Find the building’s height. The height of the part of the building above the transit is approximately 121 feet. Thus, the height of the building is determined by adding the transit’s height, 5 feet, to 121 feet. The building’s height is approximately 126 feet.

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**International Studies Charter School. Right Triangle Trigonometry**

Mrs. Rivas International Studies Charter School. Pre-Calculus Section 4.3 Right Triangle Trigonometry

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**International Studies Charter School. Right Triangle Trigonometry**

Mrs. Rivas International Studies Charter School. Pre-Calculus Section 4.3 Right Triangle Trigonometry

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Mrs. Rivas Check Points 1-7 and Pg # 8-54 Even

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