Rose-Hulman’s Homework Hotline 1 Trigonometry Study Guide
Trigonometry Study Guide
Trigonometric Function Graphs
y=sin(θ) y=cos(θ) y=tan(θ)
y=csc(θ) y=sec(θ) y=cot(θ)
Trigonometric Functions
sin (θ)
= opposite = y csc (θ) = hypotenuse = r = 1
hypotenuse r opposite y sin (θ)
cos (θ)
= adjacent = x sec (θ) = hypotenuse = r = 1
hypotenuse r adjacent x cos (θ)
sin (θ) = opposite = y cot (θ) = adjacent = x = 1
adjacent x opposite y
tan (θ)
=
tan (θ) cos (θ)
Special Right Triangles
°45°45
1
2
2
2
2
°30
°60
3
2
1
2
1
Pythagorean Theorem
Pythagorean Theorem
c2 = a2 + b2
Converse of the Pythagorean Theorem
− If c2 =a2 + b2 , then triangle ABC is a right
triangle
− If c2 < a2 + b2 , then triangle ABC is an
acute triangle
− If c2 > a2 + b2 , then triangle ABC is
an obtuse triangle
a
c b
A
B C
90°
x
y
θ
P=(x,y)
x
y
r
θ
=θ+
22
sec tan 1
θ
+θ=
22
sin cos 1
θ
=+
22
csc cot 1
Identities
Functions for Special Triangles
Angle sin θ cos θ tan θ csc θ sec θ cot θ
0° 0 1 0 Undefined 1 Undefined
30° 2
45° 1 1
60° 2
90° 1 0 Undefine d 0 Undefined 1
120° -2
135° -1 -1
150° 2
180° 0 -1 0 Undefined -1 Undefined
210° -2
225° 1 1
240° -2
270° -1 0 Undefined 0 Undefine d -1
300° 2
315° -1 -1
330° -2
360° 0 1 0 Undefined 1 Undefine d
12 32 33 3233
22 2
22 2
12
32 333 233
12
−
32 3−233
33−
22 22−22−
32−33−
12 3−233−
12
−
32−33 3233−
22−22−2−2−
32−12
−
333 233−
32−12 3−33−233−
22−22 22−
12
−
32 33−3−233
