Warm UP
Graph arcsin(x) and the limited version of
sin(x) and give their t-charts, domain, and
range
Math
IV
Lesson
36
Essential Question:
What are the inverse trig functions, and How
can I use them to simplify trigonometric
Equations?
Standard(s):
Standards: MM4A8. Students will investigate and
use inverse sine, inverse cosine, and inverse
tangent functions.
a. Find values of the above functions using
technology as appropriate.
b. Determine characteristics of the above functions
and their graphs.
Review
Graph arccos(x) and the limited version of
cos(x) and give me their domain and Range
Review
Graph the limited version of tan(x) and
arctan(x) and give me the domain and range
Quiz: Graph the following and give
the domain and range
1. limited version of sin(x)
2. Graph arcsin(x)
3. limited version of cos(x)
4. Graph arccos(x)
5. limited version of tan(x)
6. Graph arctan(x)
Bonus - arccos( -1) =
Introduction to solving
Trigonometric equations
Your preliminary goal in solving a trigonometric equation is
to isolate the trigonometric function in the equation.
To solve a trigonometric equation, use standard algebraic
techniques such as collecting like terms and factoring.
For example, to solve the equation 2 sin x = 1, divide each
side by 2 to obtain
How many solutions are there to trig
equations
….. well how many times can you go around
the unit circle?
However, We will be talking about solving trig
equations on the interval from [0,2ㅠ]
Methods to solving equations
Finding the angles that make the statement true.
Several methods for solving these types of equations
that are similar to methods used with polynomials.
–Combining like terms
–Taking square roots
–Factoring
remember cos(Ө) = x , sin(Ө) = y and
tan(Ө) = y/x
Using the unit circle to get exact values, solve
for x, [0, 2π):
1.cos x = ½
2.sin x = 0
3.tan x = ±√3
4.cos x = -1
Many times you will have to manipulate the
equation to solve
1.Combining like terms
2.Using identities to simplify
3.Factoring
Try these:
Solve for x:
0 = 4x – 2
0 = 4sin x – 2
Now try these:
Solve for x:
2
0 = 2x + 3x + 1
2
0 = 2cos x + 3cos x + 1
4sin2 x – 3 = 0
sin x – cos x sin x = 0
sin x (sec2 x + 1) = 0
2sin2 x = 2 + cos x
A Few Rules:
1.Look for values on the unit circle
2.When taking the square root, don’t forget the + and –
3.Never divide by a variable , move to the other side of the
equation and factor!
Given 3tan3 x = tan x
Subtract tan from both sides 3tan3 x – tan x = 0
Factor tan x(3tan2 x – 1) = 0
Solve: tan x = 0 or 3tan2 x – 1 = 0
tan2 x = 1/3