January 20, 2017
Precalc Warm Up # 5-5
Use the right triangle to find the five other trig rations of the
acute angle x.
1. tan x = 3
2
2. sec x = 3
January 20, 2017
Fundamental Trig Identities
What we know:
sin2x + cos2x = 1
sin x
tan x = cos
x
1
csc x = sin x
1
sec x = cos
x
1
cot x = tan
x
We can use this to show a lot of different things
and solve different things. For example, we
know then that cot x = cos x
sin x
January 20, 2017
Other pythagorean Identities.
Divide by sin2x:
Divide by cos2x:
sin2x + cos2x = 1
sin2x + cos2x = 1
January 20, 2017
Find csc x given that tan x = - 6 and sin x > 0
January 20, 2017
sinx cos2x – sinx
sin x cos2x – sin x = sin x (cos2x – 1)
= sin x (1- sin2x - 1)
= - sin3x
January 20, 2017
Factor the following:
a. sec2x – 1
b. 4tan2 x + tan x – 3
January 20, 2017
Simplify sin x + cot x cos x
January 20, 2017
Combine expressions
sin x
1+ cos x
+
cos x
sin x
January 20, 2017
Rewrite so it isn't a fraction
1
1+ sin x
January 20, 2017
Classwork and Homework