Warm Up 1/15
Solve for x, the missing side, in the triangles below.
1.
2.
Announcements
• Test on Friday
• Online homework 10-3 due Sunday Night
Inverse Trig Functions
SIDE
•If we know the ________
lengths of
a triangle, but not the
________measures
we can use
ANGLE
___________
INVERSE trig functions to solve
for θ.
•
Inverse Trig Functions
•sin-1
•cos-1
•tan-1
**Used to find angle
measures
**Located in the Trig
button section
How it Works
•If sin(θ) = 5/9, then θ = sin-1(5/9)
•Plugging into our calculator we get
• sin-1(5/9) = _______
Now You Try!
(Round to the nearest degree)
• 1. sin(A) = 4/6
A = ____________ = ________
• 2. cos(B) = 5/7
B = ____________ = ________
• 3. tan(R) = 1
R = ____________ = _______
• 4. sin(Z) = 8/9
Z = ____________ = ________
• 5. cos(θ) = 3/12
θ = ____________ = ________
• 6. tan(X) = 15/5
X = ____________ = ________
Important Side Note
• ***Sometimes you will see the inverse trig
functions written as arcsin, arccos, and
arctan….they do the exact same thing!
Finding a Missing Angle
1. Mark the __________
ANGLE that you are looking for.
SIDES in relation to the angle that you
2. Label the given ________
need to find.(opp, adj, hyp)
TRIG FUNCTION (sin, cos, or tan)
3. Decide which _____________________
you can write with the sides that you have been given.
EQUATION
4. Write out the __________________.
INVERSE TRIG (sin-1, cos-1, or tan-1) to tell you
5. Use __________________
the missing angle measure.
EXAMPLES
EX 1 Find the missing angle, “x”
5
14
x
1.
2.
3.
4.
5.
Mark the angle that we are looking for, x.
Label the given sides in relation to x. (opp, hyp)
Decide which trig function goes with Opp, Hyp (sin)
Write out the equation.
Use your calculator to tell you the degree measure.
EXAMPLES
EX 2 Find the missing angle, “x”
5
x
14
1.
2.
3.
4.
5.
Mark the angle that we are looking for, x.
Label the given sides in relation to x. (opp, adj)
Decide which trig function goes with Opp, Adj (tan)
Write out the equation.
Use your calculator to tell you the degree measure.
Homework
• Online HW 10-3
Classwork
• Pg. 439 #12-17, 20-22