Presentation on theme: "4.3 Right Triangle Trigonometry"— Presentation transcript:
1 4.3 Right Triangle Trigonometry Objectives:Evaluate trigonometric functions of acute anglesUse trig identitiesEvaluate trig functions with a calculatorUse trig functions to model and solve real life problems
2 Right Triangle Trigonometry Using the lengths of these 3 sides, we form six ratios that define the six trigonometric functions of the acute angle θ.sine cosecantcosine secanttangent cotangent*notice each pair has a “co”Side opposite θhypotenuseθSide adjacent to θ
3 Trigonometric Functions Let θ be an acute angle of a right triangle.hypotenuseRECIPROCALSoppositeθadjacent
4 Evaluating Trig Functions Use the triangle to find the exact values of the six trig functions of θ.Repeat for β. What do you notice?sin 𝜃= csc 𝜃=cos 𝜃= sec 𝜃=tan 𝜃= cot 𝜃=sin 𝛽= csc 𝛽=cos 𝛽= sec 𝛽=tan 𝛽= cot 𝛽=54θ3
5 Solving Right Triangles with Trig Use the trig functions to find the missing sides for θ = 57°Use the trig functions to find the missing sides for θ = 32°h5θh17xθ2xθθaθ27ox1003θ
7 Evaluating Trig Functions for 45° Find the exact value of the following:sin 45° =cos 45° =tan 45° =45°
8 Evaluating Trig Functions for 30° and 60° Find the exact values of the following:sin 60° = • sin 30° =cos 60° = • cos 30° =tan 60° = • tan 30° =60°
9 Sine, Cosine, and Tangent of Special Angles Θ in Degrees30°60°45°Θ in Radiansπ 6π 3π 4sin Θ3 21 22 2cos Θtan Θ3 331
10 Applications of Right Triangle Trigonometry Angle of elevation: the angle from the horizontal upward to the objectAngle of depression: the angle from the horizontal downward to the object
11 Word ProblemsA surveyor is standing 50 feet from the base of a large tree. The surveyor measure the angle of elevation to the top of the tree as 71.5°. How tall is the tree?
12 You are 200 yards from a river You are 200 yards from a river. Rather than walk directly to the river, you walk 400 yards along a straight, diagonal path to the river’s edge. Find the acute angle θ between this path and the river’s edge.