Inverse Trigonometric Functions

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Presentation transcript:

Inverse Trigonometric Functions Essential Question: What are the inverse trig. functions? How are they used to find the missing angles of triangles? Assessment: Demonstrate in writing in summary of notes.

Methods that we already know when working with right triangles: To find a missing angle: Triangle sum Theorem To use the Triangle Sum Theorem, you must already know 2 angle measures. Essential Question: What are the inverse trig. functions? How are they used to find the missing angles of triangles? Assessment: Demonstrate in writing in summary of notes.

Inverse trig ratios can be used to find missing angle measures if you have a right triangle, and know two side lengths. Each of the 3 trig ratios has an inverse. They are 𝑠𝑖𝑛 −1 (read sine inverse), 𝑐𝑜𝑠 −1 (read cosine inverse), and 𝑡𝑎𝑛 −1 (read tangent inverse). Essential Question: What are the inverse trig. functions? How are they used to find the missing angles of triangles? Assessment: Demonstrate in writing in summary of notes.

Sine inverse is used if you know the OPPOSITE and the HYPOTENUSE Sine inverse is used if you know the OPPOSITE and the HYPOTENUSE. Cosine inverse is used if you know the ADJACENT and the HYPOTENUSE. Tangent inverse is used if you know the OPPOSITE and the ADJACENT. Essential Question: What are the inverse trig. functions? How are they used to find the missing angles of triangles? Assessment: Demonstrate in writing in summary of notes.

Essential Question: What are the inverse trig. functions Essential Question: What are the inverse trig. functions? How are they used to find the missing angles of triangles? Assessment: Demonstrate in writing in summary of notes.

Essential Question: What are the inverse trig. functions Essential Question: What are the inverse trig. functions? How are they used to find the missing angles of triangles? Assessment: Demonstrate in writing in summary of notes.

Essential Question: What are the inverse trig. functions Essential Question: What are the inverse trig. functions? How are they used to find the missing angles of triangles? Assessment: Demonstrate in writing in summary of notes.

Essential Question: What are the inverse trig. functions Essential Question: What are the inverse trig. functions? How are they used to find the missing angles of triangles? Assessment: Demonstrate in writing in summary of notes.

When a problem says to solve a triangle, you must find all sides and all angles. Remember: Use trig functions to find side lengths AND inverse trig functions to find angle measures. Essential Question: What are the inverse trig. functions? How are they used to find the missing angles of triangles? Assessment: Demonstrate in writing in summary of notes.

Two students are observing a hot air balloon Two students are observing a hot air balloon. The balloon is attached to the ground by a rope that is 50 feet long. Student A is 60 feet away from where the rope is attached to the ground. Student B observes the balloon at an angle of elevation of 60°. The diagram below represents this situation. Part A: To the nearest tenth of a foot, how far away from Student A is the balloon? Essential Question: What are the inverse trig. functions? How are they used to find the missing angles of triangles? Assessment: Demonstrate in writing in summary of notes.

Part B: To the nearest tenth of a foot, how far away from Student B is the balloon? Essential Question: What are the inverse trig. functions? How are they used to find the missing angles of triangles? Assessment: Demonstrate in writing in summary of notes.

Part C: The balloon rises vertically so that the distance between the balloon and Student A is 90 feet. By how many feet did the balloon rise? Express your answer to the nearest foot. Essential Question: What are the inverse trig. functions? How are they used to find the missing angles of triangles? Assessment: Demonstrate in writing in summary of notes.

Part D: After the balloon rises so that the distance between the balloon and Student A is 90 feet, what is the angle of elevation from Student A to the balloon? Express your answer to the nearest tenth of a degree. Essential Question: What are the inverse trig. functions? How are they used to find the missing angles of triangles? Assessment: Demonstrate in writing in summary of notes.