Trigonometric Function Flashcards
the questions ask for
sin θ = ??
sin θ = y/r
r = sqrt(x^2 + y^2)
cos θ = ??
cos θ = x/r
r = sqrt(x^2 + y^2)
tan θ = ???
tan θ = y/x
csc θ = ??
csc θ = r/y
r = sqrt(x^2 + y^2)
sec θ = ??
sec θ = r/x
r = sqrt(x^2 + y^2)
cot θ = ??
cot θ = x/y
What if the question asks you to express the given trigonometric functions in terms of the same function of a positive acute angle??
sin 160 = ??
cos 250 = ??
for sin 160
180 - 160 = 20
is in the Q2 (starts from the left of the Q1 where -x,y is)
so sin(20)
for cos 250
it must be -cos(70)
it is not 270 - 250 = 20
is
250 - 180 = 70
why? Because cosine is measured from the x-axis
why negative? because the x is negative in Q2.
when getting the reference angle for sine and cosine, what should you know?
SINE is correlate with Y axis
COSINE is correlate with X axis
so ….
if the y is negative in the quadrant, it become a negative.
and when minusing, you must minus from the nearest vertical (y) axis for SINE and horizontal for COSINE (x)
how do you find the radians?
radian = degree * pi/180
to find degree
degree = radian ^ 180/pi
What does the complement refer to?
it refers to the angle that adds up to the quadrant degree like 90
so if angle = 58 degrees
complement is 90-58
32 degrees is the complement angle.
What does the supplement refer to?
add up to 180
how do you find rad or degree?
rad = degree * pi/180
degree = rad * 180/pi
cot theta = 1/9, how would you find sec and sin theta?
cot theta = x/y
so x = 1
y = 9
so find r = sqrt(82)
now sub it in in sec and sin.
how about tan theta = 1.073, how can you find sin theta and sec theta?
ez
make 1.073 to fraction
1073/1000
now you have x and y. 1073,1000.
SOH, CAH, TOA
sin = opposite of a / hypotenuse
cos = adjacent of a / hypotenuse
tan = opposite/adjacent
word question: When the question says the bottom of the face is 31 degrees, the top is 34 degrees, and the mountain’s base is 270, what does it look like?
ez
There’s a triangle for 31 degrees with the base as 270
Another one is for 34 degrees with the base at 270.
always draw it visually and act accordingly to the question.
What is the sine rule?
sin A / a = sin B / b (for angle)
a / sin A = b / sin B (for side)
What is the cosine rule?
In the cheat sheet, too much.
How do you solve the distance between things using bearing?
Make a huge compass, then label it.
Then make angles
determine the signs of the given function
cos 331
csc 260
refer to the quadrants
Cos is relate to X so follow the angle and see what x position is, is positive.
csc is relate to sin
and sin relate to y
so follow and see where the y lands, is negative
so cos 331 is positive
and csc 260 is negative.
determine the quadrants in which the terminal side of the angle lies
cos theta = 0.9500
cos theta = -0.9500
this makes x/r
x is negative and r is positive
when x is negative, it is in QII and QIII, that the answer.
where is the negative quadrant and positive quadrant for tan?
for tan
QI = positive
QII = negative
QIII = positive
QIV = negative
Find the common quad for
csc theta < 0, tan theta < 0
csc theta relates to sin
sin is y
is says less than 0, meaning negative
that means QIII and QIV is negative
for tan, also negative, QII and QIV
the common quad is
QIV
decide whether the given ratio is positive and negative
II, x/y
visit the quad
QII is x negative and y positive
so when negative and positive combined or - and +, it becomes negative, so negative.
in case of r/x , r is always positive.
