Math 124
Does the initial side define an angle
No
What makes an angle in standard positon
An angle is in standard position when the vertex is on the origin and any one of the rays lies on the x-axis
What is an angle that's measures goes downwards and is under the horizontal line called?
An angle of depression
What is the name of an angle thats measure goes upward and is above the horizontal line
An angle of elec vation
What makes a negative and a postive angle coterminal?
A negative and a positve angle are coterminal if the amount that the negative angle is less than 0 or -360 degrees is equal to the amount that the positive angle is less than 360 degrees, or if the amount that the negative angle is greater than -360 degrees is equal to the amount that the positive angle is greater than 0 or 360 degrees
How do you find the value of a reciprocal
You can either flip the formula Ex: sin=opposite/hyp reciprocal of sin (cosecant)= hyp/opp Or you can put a 1 over the value= sin=4/1 cosecant= 1/4
How do you find the measure of the angle of elevation or depression in a right triangle?
You first use the function that consist of both the given sides (Such as tan,etc.) then multiply what that function equals by the inverse version of the function. For Example: If you have the opposite and adjacent, you can use tan, you then find what the opposite divided by the adj equals and then multiply that by tan^-1/
In which way do you measure an angle
You measure from the initial side to the terminal side
What variable represents the opposite
a
What variable represents the adjacent
b
What variable represent the hyp
c
What is the complement of an angle
the angle that needs to be added to another angle to make 90 degrees. Ex: 90-50=40 40+50=90 the complement of 50 degrees is 40 degrees
what makes two positive angles coterminal
two positive angles are coterminal if the amount one is greater than 0 degrees is equal to the amount the other is greater than 360 degrees. Ex: 120 degrees is coterminal to 480 degrees.
What does Cah in Soh Cah Toa mean
Cosine=Adjacent÷Hypotenuse
What is the reciprocal of tangent
Cotangent (cot)
What makes an angle negative?
If it moves in the clockwise direction it's negative
What makes an angle positive
If it moves in the counter clockwise direction it's positive
Why do you measure an angle beginning from the initial side and going to the terminal side
It's because the initial side is in the original position, making it in the position the rays were in before any rotation. So if you measure beginning from the initial side it is easier to calculate how much the terminal ray moved and in which way (clockwise or counter clockwise)
What is the reference angle in a unit circle
It's the acute angle that is in between the terminal side of the angle and the x-axis.
how do you find 6 trig functions
Just find sin, cos, and tan, and their reciprocals or vice versa.
What does Soh in Soh cah Toa mean
Sine= OPPOSITE÷HYPOTENUSE
What does SOH CAH TOA mean?
Sine=Opposite÷Hyp Cosine=Adjacent÷Hyp Tangent= Opposite÷Adjacent
What does Toa in Soh Cah Toa mean
Tangent=Opposite÷Hypotenuse
What is the adjacent
The adjacent side is the side that is next to the given angle and is not the hypotenuse or opposite
What is a supplement of an angle?
The amount that needs to be added to an angle for it to equal 180 degrees
What are the requirements for an angle to be considered a reference angle
The first requirement is that the reference angle always has to be positive, meaning that it is moving in a counter clockwise direction. The second requirement is that it has to be an acute angle, meaning that it has to be less than 90 degrees.
What is the hypotenuse
The longest side in a right triangle
What is the opposite
The opposite is always going to be the angle that on the opposite side of a given angle
What is a vertex
The point of the angle where the two rays meet
What is the reciprocal of cosin (cosine)
The reciprocal of cosin is secant (Sec)
What is the reciprocal of sin (sine)
The reciprocal of sin is csc (cosecant)
What is the initial side of an angle
The side of an angle that is in the original position and clearly has not moved
Which side in angle defines the angle
The terminal side
What is the terminal side of an angle
The terminal side of an angle is the side of the angle that is not in the original position (has moved)
How do you solve for a value of an unknown side
To solve for the value of an unknown side basically you just use the function which uses the side that you know and the side that you're trying to find. You then cancel out the denominators by multiplying on both sides and try to get a value and the missing side each on one side alone.
What are "supplementary angles?"
Two angles that add up to 180° Ex: 130 degrees and 50 degrees add up to 180 degrees, therefore they are complementary angles
What are complementary angle
Two angles that add up to 90 degrees Ex: 45 degrees and 45 degrees add up to 90 degrees, therefore they're complementary angles
What are coterminal angles
Two angles that land on the same spot in a unit circle
what makes two negative angles co-terminal?
Two negative angles are coterminal if the amount one is less than 0 degrees is equal to the amount one is less than 360 degrees. Ex: -480 degrees and -120 degrees are coterminal.
