mrs. rivas international studies charter school
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Mrs. Rivas
International Studies Charter
School.
Pre-Calculus Section
4.3
RIGHT TRIANGLE TRIGONOMETRY
Geometry Review
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
Trigonometry Functionsππ½
π
π = hypotenuse
= opposite side
= adjacent side
π¬π’π§ π½=ππ
ππ¨π¬π½=ππ
πππ§ π½=ππ
πΉππππππππππ
ππ¬ππ½=ππ
π¬πππ½=ππ
ππ¨π π½=ππ
SOHCAHTOA
Examples: What are the sine, cosine and tangent ratios for T.
Trigonometry Functions
Examples: What are the secant, cosecant and cotangent ratios for T.
Trigonometry Functions
ππ¬ππ»=πππππππππππππππππππ
π¬πππ»=ππ ππππππ
πππππππππππ
ππ¨ππ»=ππππππππππ ππππππ
Examples: Find the value of . Round to the nearest tenth.
Sin 35ΒΊ = x20
2020
20 0.5735 = x11.47 = x
11.5 β x
Trigonometry Functions
Mrs. Rivas
International Studies Charter
School.
Pre-Calculus Section
4.3
RIGHT TRIANGLE TRIGONOMETRYUse right triangles to
evaluatetrigonometric functions
Mrs. Rivas
International Studies Charter
School.
Pre-Calculus Section
4.3
RIGHT TRIANGLE TRIGONOMETRY
Mrs. Rivas
International Studies Charter
School.
Pre-Calculus Section
4.3
RIGHT TRIANGLE TRIGONOMETRY
Mrs. Rivas
International Studies Charter
School.
Pre-Calculus Section
4.3
RIGHT TRIANGLE TRIGONOMETRY
Mrs. Rivas
International Studies Charter
School.
Pre-Calculus Section
4.3
RIGHT TRIANGLE TRIGONOMETRY
Find function values for , ,
Mrs. Rivas
International Studies Charter
School.
Pre-Calculus Section
4.3
RIGHT TRIANGLE TRIGONOMETRY
Mrs. Rivas
International Studies Charter
School.
Pre-Calculus Section
4.3
RIGHT TRIANGLE TRIGONOMETRY
Mrs. Rivas
International Studies Charter
School.
Pre-Calculus Section
4.3
RIGHT TRIANGLE TRIGONOMETRY
Mrs. Rivas
International Studies Charter
School.
Pre-Calculus Section
4.3
RIGHT TRIANGLE TRIGONOMETRY
Use equal cofunctions of complements
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 4.36. Because the sum of the angles of any triangle is 180Β°, in a right triangle the sum of the acute angles is 90Β°. Thus, the acute angles are complements.
If the degree measure of one acute angle is , then the degree measure of the other acute angle is .
This angle is shown on the upper right in Figure 4.36.
Two positive angles are complements if their sum is 90Β°or . For example, angles of and are complements because .
Mrs. Rivas
International Studies Charter
School.
Pre-Calculus Section
4.3
RIGHT TRIANGLE TRIGONOMETRY
Letβs use Figure 4.36 to compare and .
Thus, . 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 complementβs sine.
Mrs. Rivas
International Studies Charter
School.
Pre-Calculus Section
4.3
RIGHT TRIANGLE TRIGONOMETRY
Any pair of trigonometric functions and for which
and
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.
Mrs. Rivas
International Studies Charter
School.
Pre-Calculus Section
4.3
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.
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 22Β°. The transit is 5 feet above the ground and 300 feet from the building. Find the buildingβs 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 transitβs height, 5 feet, to 121 feet.
The buildingβs height is approximately 126 feet.
Mrs. Rivas
International Studies Charter
School.
Pre-Calculus Section
4.3
RIGHT TRIANGLE TRIGONOMETRY
Mrs. Rivas
International Studies Charter
School.
Pre-Calculus Section
4.3
RIGHT TRIANGLE TRIGONOMETRY
Mrs. Rivas
Check Points 1-7 and Pg. 498-499 # 8-54 Even
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