Trigonometry Rules Flashcards
Sin(θ)/cos(θ)
Tan(θ)
(cosθ)^2 + (sinθ)^2
1
Sin 45
√2 / 2
Cos45
√2 / 2
Tan 45
1
Sin 60
√3 / 2
Cos 60
1/2
Tan 60
√3
Sin 30
1/2
Cos 30
√3 / 2
Tan 30
√3 / 3
Sin 90
1
Cos 90
0
Tan 90
undefined
Sin 0
0
Cos 0
1
Tan 0
0
If you drew the whole trig triangle in a circle thing, which bit would be cos?
The horizontal line that goes over the x axis
If you drew the whole trig triangle in a circle thing, which bit would be sin?
The vertical line that starts where the cos line away from the origin ends and carries on going away.
If you drew the whole trig triangle in a circle thing, which bit would be tan?
It’s the tangent to the circle that starts (at one of the points) where the circle touches the x axis.
What’s the radius of the circle in the trig triangle in circle thing?
1
In the general ABC triangle, what are the sides called? Please start from the one opposite A.
a, b, and c
a/sinA
b/sinB= 2*r(adius)
sin A/a
sinB/b= 1/2r
a
√(b^2+c^2-2bcCosA)
cosA
(b^2+c^2-a^2)/2bc
Area of a general triangle
(bcSinA)/2
Sin(x) (simple relation to Cos)
Cos(90-x) AKA Cos (-(x-90))
Cos(x) (simple relation to Sin)
Sin(90-x)
tan(x) (reworded only using tan)
1/tan(90-x)
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).
All Stations To Chalfont
(All Sin Tan Cos)
if Sin(x) was positive, then what would be equal to Sin(x)?
Sin(180-x)
if Cos(x) was positive, then what would be equal to Cos(x)?
Cos(360-x)
if Tan(x) was positive, then what would be equal to Tan(x)?
Tan(180+x)
In which direction is a positive angle (eg 30, 170, 330 etc.) measured?
anticlockwise
Sin(x) is positive, is that true for Sin(-x)?
No Sin(-x) is negative
Can you tell me the periods for the graphs?
Sin and Cos: 360; Tan:180
Tan(x) is positive, is that true for Tan(-x)?
No Tan(-x) is negative
Cos(x) is positive, is that true for Cos(-x)?
Yes Cos(-x) is positive
Can you tell me the max/mins for the graphs?
Sin and Cos: 1,-1; Tan: infinitely stretching upwards.
What are the untouchable χs on a Tan graph called?
Asymptotes
What are the trigs at the end of the day? (Sin, Cos, and Tan)
Functions. You can treat them as such?
How would one go about finding the midpoint of a triangle? (or the circumcentre i guess?)
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.
