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Lesson 5-5
[Book: 15-25 ALL, 28-31 ALL, 36-39 ALL, 45a, 46, 52-54 ALL, 58-60 ALL]
Objectives
1.
2.
3.
If you look at the chart on page 305, you will see that when we take the sine, cosine, or
tangent of a(n) ____________, we get a(n) _____________.
Today, we will talk about what we have to do if we already know a(n) ______________,
and we have to find a(n) __________________.
Let’s demonstrate using a 30-60-90 triangle.
So, if we already know the trigonometric ratio, we must use the __________________ of
the trigonometric function in order to find the unknown angle.
INVERSE TRIGONOMETRIC FUNCTIONS
+
+
+
*Check the table on page 306
Ex. 1 Solve each equation.
b) sin x = 
a) tan x = 1
1
2
Ex. 2 Evaluate each expression. Assume all angles are in Quadrant I.
a) tan (tan -1
6
)
11
b) tan (arccos
4
)
5
We can also use the inverse trig functions on our calculator to find missing parts of a
right triangle. If we are using the inverse sine, cosine, or tangent, what part of a triangle
are we trying to find?
Ex. 3 If g = 28 and h = 21, find H.
Ex. 4 If a 100-foot building casts an 88-foot shadow. What is the angle of elevation of
the sun?
Solve a triangle
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Ex. 5
Solve Triangle JKL when given the following descriptions.
a) K = 40
k = 26
b) j = 65   55
Name ________________________________
Date _____________
Quiz – 5-1 through 5-4
Advanced Math
Directions: You have 10 minutes to take this quiz. You may NOT use any resource
other than your own brain.
1. How many seconds are in a degree?
2. If we draw an angle by making 2 full counterclockwise rotations, then how many
degrees is that angle?
3. Find one angle that is coterminal to 60 degrees.
4. Draw a unit circle or a reference triangle and find sec 30 .
5. If A = 38 and a = 14, find c to the nearest tenth.