Transcript Essential Question

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.
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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).
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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.
Cosine inverse is used if you know the
ADJACENT and the HYPOTENUSE.
Tangent inverse is used if you know the
OPPOSITE and the ADJACENT.
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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? 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?
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? How are
they used to find the missing angles of triangles?
Assessment: Demonstrate in writing in summary of notes.
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•
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. 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?
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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.
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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.
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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.