5.1--Fundamental Identities
sin 30o =
30o
x 2
45o
cos 45o =
x
2x
x 3
45o
tan 60o =
x
x
sin 13o = cos _____
tan 70o = cot _____
sin2x + cos2x = 1
60o
tan2x + 1 = sec2x
5.1--Fundamental Identities
y = sin x
sin +
all +
tan +
cos +
y = cos x
y = tan x
Evaluate the remaining trig functions using the info. provided:
1) sin θ = 3/8, cos θ < 0
2) sec θ = -11/2, cot θ > 0
sin θ = 3/8
sin θ =
cos θ =
cos θ =
tan θ =
tan θ =
cot θ =
cot θ =
sec θ =
sec θ = -11/2
csc θ =
csc θ =
5.1--Fundamental Identities
3)
If tan θ = 2.113, find cot (π/2 - θ):
4)
If sin (θ - π/2) = 0.561, find cos (-θ):
5)
Simplify:
6)
Simplify:
sin3x + sin x cos2x
(sec x + 1)(sec x - 1)
sin2x
5.1--Fundamental Identities
7)
Simplify:
cos x
1 - sin x
8)
-
sin x
cos x
Find all solutions for the equation over the interval [0, 2π):
cos3x
sin x
= cot x
5.1--Fundamental Identities
9)
Find all solutions for the equation over the interval [0, 2π):
2 sin2x + sin x = 1
10)
Make the suggested trig substitution, then simplify using
one of the Pythagorean identities:
25 - x2 ,
x = 5 sin θ