General Trigonometry

Question 1

Formula for Radians to Degrees

Answer 1

180/pi

Question 2

Exact Trig evaluations for 30degrees/ pi/6

Answer 2

sin=1/2, cos=rad3/2, tan=1/rad3, cot=rad3, sec=2/rad3, csc=2

Question 3

Exact Trig evaluations for 45degrees/ pi/4

Answer 3

sin=1/rad2, cos=1/rad2, tan=1, cot=1, sec=rad2, csc=rad2

Question 4

Exact Trig evaluations for 60degrees/ pi/3

Answer 4

sin=rad3/2, cos=1/2, tan=rad3, cot=1/rad3, sec=2, csc=2/rad3

Question 5

Finding reference angles in quadrants I-IV

Answer 5

QI: theta=angle, QII: theta=180-angle, QIII: theta= 180+angle, QIV: theta=360-angle

Question 6

Law of Sines

Answer 6

SinA/a = SinB/b = SinC/c

Question 7

Law of Cosines

Answer 7

a^2 = b^2 + c^2 -2bcCosA
b^2 = a^2 + c^2 -2acCosB
c^2 = b^2 + a^2 -2baCosC
&
CosA = (b^2 + c^2 - a^2) / 2bc
CosB = (a^2 + c^2 - b^2) / 2ac
CosC = (b^2 + a^2 - c^2) / 2ba

Question 8

Pythagorean Idetities

Answer 8

sin^2x+cos^2x = 1
1+tan^2x = sec^2x
1+cot^2x = csc^2x

Question 9

Double Angle Formulas

Answer 9

Sin(2x) = 2sinxcosx
Cos(2x) = cos^2x + sin^2x
Cos(2x) = 2cos^2x - 1
Cos(2x) = 1 - 2sin^2x
Tan92x) = (2tanx)/(1-tan^2x)

Question 10

Reduction Formula

Answer 10

Cos^2x = (1+cos2x)/2
Sin^2x = (1-sin2x)/2
Tan^2x = (1-cos2x)/(1+cos2x)

Question 11

inverse trig functions (arc=inverse)
Domains & Ranges
1. arcsin 2. arccos 3. arctan
4. arccot 5. arcsec 6. arccsc

Answer 11

1. [-1,1] [-pi/2, pi/2]
2. [-1,1] [0, pi]
3. (-i, i) (-pi/2, pi/2)
4. (-i, i) (o, pi)
5. (-i, -1]U[1, i) [0, pi/2) U (pi/2, pi]
6. (-i, -1]U[1, i) [-pi/2, 0) U (0, pi/2]

Question 12

for all:

1. cot-1cotx =x 2. cotcot-1x =x
2. sec-1secx =x 4. secsec-1x =x
3. csc-1cscx =x 6. csccsc-1x =x

Answer 12

1. xE (0,pi)
2. xE (-i, i)
3. xE [0, pi/2) U (pi/2, pi]
4. xE (-i, -1] U [1, i)
5. xE [-pi/2, 0) U (0, pi/2]
6. xE (-i, -1] U [1, i)

Question 13

RANGE of inverse function =

Answer 13

DOMAIN of restricted function

Question 14

magnitude of lUl (vector)

Answer 14

rad a^2 + b^2

Question 15

vector U + vector V =

Answer 15

(a + c, b + d)

Question 16

Vector U - vector V =

Answer 16

(a - c, b - d)

Question 17

vertical vector llUllsin0, horizontal vector llUllcos0

Answer 17

With unknown direction angle:
Uv = U/llUll = 
or
With known direction angle:
V =   llVll = rad a^2 + b^2