Trigonometry Rules

Question 1

Sin(θ)/cos(θ)

Answer 1

Tan(θ)

Question 2

(cosθ)^2 + (sinθ)^2

Answer 2

1

Question 3

Sin 45

Answer 3

√2 / 2

Question 4

Cos45

Answer 4

√2 / 2

Question 5

Tan 45

Answer 5

1

Question 6

Sin 60

Answer 6

√3 / 2

Question 7

Cos 60

Answer 7

1/2

Question 8

Tan 60

Answer 8

√3

Question 9

Sin 30

Answer 9

1/2

Question 10

Cos 30

Answer 10

√3 / 2

Question 11

Tan 30

Answer 11

√3 / 3

Question 12

Sin 90

Answer 12

1

Question 13

Cos 90

Answer 13

0

Question 14

Tan 90

Answer 14

undefined

Question 15

Sin 0

Answer 15

0

Question 16

Cos 0

Answer 16

1

Question 17

Tan 0

Answer 17

0

Question 18

If you drew the whole trig triangle in a circle thing, which bit would be cos?

Answer 18

The horizontal line that goes over the x axis

Question 19

If you drew the whole trig triangle in a circle thing, which bit would be sin?

Answer 19

The vertical line that starts where the cos line away from the origin ends and carries on going away.

Question 20

If you drew the whole trig triangle in a circle thing, which bit would be tan?

Answer 20

It’s the tangent to the circle that starts (at one of the points) where the circle touches the x axis.

Question 21

What’s the radius of the circle in the trig triangle in circle thing?

Answer 21

1

Question 22

In the general ABC triangle, what are the sides called? Please start from the one opposite A.

Answer 22

a, b, and c

Question 23

a/sinA

Answer 23

b/sinB= 2*r(adius)

Question 24

sin A/a

Answer 24

sinB/b= 1/2r

Question 25

a

Answer 25

√(b^2+c^2-2bcCosA)

Question 26

cosA

Answer 26

(b^2+c^2-a^2)/2bc

Question 27

Area of a general triangle

Answer 27

(bcSinA)/2

Question 28

Sin(x) (simple relation to Cos)

Answer 28

Cos(90-x) AKA Cos (-(x-90))

Question 29

Cos(x) (simple relation to Sin)

Answer 29

Sin(90-x)

Question 30

tan(x) (reworded only using tan)

Answer 30

1/tan(90-x)

Question 31

Can you please give me a nifty acronym to explain which trig functions are positive in which quadrants? please start in 1st quadrant (top right).

Answer 31

All Stations To Chalfont
(All Sin Tan Cos)

Question 32

if Sin(x) was positive, then what would be equal to Sin(x)?

Answer 32

Sin(180-x)

Question 33

if Cos(x) was positive, then what would be equal to Cos(x)?

Answer 33

Cos(360-x)

Question 34

if Tan(x) was positive, then what would be equal to Tan(x)?

Answer 34

Tan(180+x)

Question 35

In which direction is a positive angle (eg 30, 170, 330 etc.) measured?

Answer 35

anticlockwise

Question 36

Sin(x) is positive, is that true for Sin(-x)?

Answer 36

No Sin(-x) is negative

Question 37

Tan(x) is positive, is that true for Tan(-x)?

Answer 37

No Tan(-x) is negative

Question 38

Cos(x) is positive, is that true for Cos(-x)?

Answer 38

Yes Cos(-x) is positive

Question 39

Can you tell me the periods for the graphs?

Answer 39

Sin and Cos: 360; Tan:180

Question 40

Can you tell me the max/mins for the graphs?

Answer 40

Sin and Cos: 1,-1; Tan: infinitely stretching upwards.

Question 41

What are the untouchable χs on a Tan graph called?

Answer 41

Asymptotes

Question 42

What are the trigs at the end of the day? (Sin, Cos, and Tan)

Answer 42

Functions. You can treat them as such?

Question 43

How would one go about finding the midpoint of a triangle? (or the circumcentre i guess?)

Answer 43

If you perpendicularly bisect all of the sides then the point where all the lines intersect will be the midpoint. It’s also the centre of that triangle’s circle.