Trigonometry

Question 1

Side lengths for 45 degree triangle

Answer 1

Hypotenuse = x√2
45 leg = x

Question 2

Side lengths for 60-30 degree triangle

Answer 2

Hypotenuse = 2x
60 leg = x√3
30 leg = x

Question 3

sin θ

Answer 3

opp / hyp

Question 4

cos θ

Answer 4

adj / hyp

Question 5

tan θ

Answer 5

opp / adj

Question 6

csc θ

Answer 6

reciprocal of sine
hyp / opp

Question 7

sec θ

Answer 7

reciprocal of cosine
hyp / adj

Question 8

cot θ

Answer 8

reciprocal of tangent
adj / opp

Question 9

sin 30

Answer 9

cos 60

Question 10

cos 30

Answer 10

sin 60

Question 11

tan 30

Answer 11

1 / tan 60 (reciprocals)

Question 12

sin 45

Answer 12

cos 45

Question 13

tan 45

Answer 13

1

Question 14

Unit Circle, 30 degree Q1 coordinate

Answer 14

(√3 / 2, 1/2)

Question 15

Unit Circle, 45 degree Q1 coordinate

Answer 15

(√2/2, √2/2)

Question 16

Unit Circle, 60 degree Q1 coordinate

Answer 16

(1/2, √3 / 2)

Question 17

Turning degrees to radians

Answer 17

degree divided by 180, include pi
degrees(pi/180)

Question 18

Turning radians to degrees

Answer 18

multiply radians by 180, then divide number by denominator.
radians(180/pi)

Question 19

Co-terminal angles

Answer 19

Angles in standard position with the same terminal side are co-terminal angles. (full 360 around both directions)
- if adding 360 does not result in positive answer, keep adding 360 and vise versa
2pi = 360

Question 20

Reference angles

Answer 20

the positive angle formed on the x-axis.
- has to touch x-axis
- need to be in quadrant 1

Question 21

Trig functions, sin θ

Answer 21

y coordinate

Question 22

Trig functions, cos θ

Answer 22

x coordinate

Question 23

Trig functions, tan θ

Answer 23

y / x
sin / cos

Question 24

Q1 positive trig functions

Answer 24

ALL

Question 25

Q2 positive trig functions

Answer 25

sin θ, csc θ

Question 26

Q3 positive trig functions

Answer 26

tan θ, cot θ

Question 27

Q4 positive trig functions

Answer 27

cos θ, sec θ

Question 28

How to look at inverse trig functions

Answer 28

sin -1 (1/2)
ask, ‘where is y equal to. . .?’ to the 1/2
look at the sign as well

Question 29

Quotient identities

Answer 29

tan θ = sin θ/cosθ
cot θ = cos θ/sin θ

Question 30

Reciprocal identities

Answer 30

sin θ = 1/csc θ
cos θ = 1/sec θ
tan θ = 1/cot θ
the same with csc, sec, cot flipped postions

Question 31

Pythagorean identities

Answer 31

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

Question 32

Helpful techniques for simplifying expressions

Answer 32

Change everything to sine or cosine
factoring to simplify expression if possible
get common denominators if there are fractions
multiply by conjugates