Unit 8 (Trigonometry)-Triangles
When using the Law of Sines, what is the a-value (when writing formulas) equal to?
"a" is the side matching the given angle, when writing formulas, it doesn't necessarily correspond to a side labeled "a"
What is the area of triangle given: a=19 B=75 c=8
((19*8)/2)Sin75 73.41
Given Triangle ABC, what is the formula to solve a triangle using the Law of Sines?
((SinA)/a)=((SinB)/b)=((SinC)/c) *Be expected to be able to solve the Law of Sines given a side and two angles, one of which matches the given side (The Law of Sines)
What is the coordinate at 240 degrees?
(-1/2 , -√3/2)
What is the coordinate at 90 degrees?
(0 , 1)
What radian measure is found in Quadrant II and has a reference angle of π/4? What is the degree measure?
(3π)/4 135
What radian measure is found in Quadrant II and has a reference angle of π/6? What is the angle measure?
(5π)/6 150
What is the value of s in Heron's Area Formula?
(a+b+c)/2
Tan(210)
(√3)/3
What is the coordinate at 30 degrees?
(√3/2 , 1/2)
Tan(315)
-1
What is Tan(135) (given that the reference angle is 45 and the angle is in Quadrant II)?
-1
What is Tan[(3π)/4] (given that the reference angle is π/4)?
-1
Cos(120)
-1/2
Sin(210)
-1/2
What is Cos(240) (given that the reference angle is 60 and the angle is in Quadrant III)?
-1/2
What is -51 degrees in radians?
-17π/60
Sin(315)
-√2/2
What is Cos(135) (given that the reference angle is 45 and the angle is in Quadrant II)?
-√2/2
What is Cos[(3π)/4] (given that the reference angle is π/4)?
-√2/2
Tan(120)
-√3
Cos(210)
-√3/2
What is Sin(240) (given that the reference angle is 60 and the angle is in Quadrant III)?
-√3/2
In an ASS Obtuse Triangle, how many triangles are formed when a<b
0
How many triangles can be formed with the given properties: c=7 b=6 B=120
0 It is an Obtuse ASS Triangle Side b has the matching angle B, so it will take the place of "a" in the formula and side c will take the place of "b" in the formula
In an ASS Acute Triangle, how many possible triangles can be formed?
0, 1, or 2
In an ASS Acute Triangle, in which a<b, how many triangles can be formed?
0, 1, or 2
How many triangles can be formed with the given properties: a=6 b=7 B=45
1
In an ASS Acute Triangle, in which a>b, how many triangles can be formed?
1
In an ASS Obtuse Triangle, how many triangles are formed when a>b?
1
Tan(45)
1
The Quantity of the Radius
1
Cos(60)
1/2
Sin(30)
1/2
What radian measure is found in Quadrant IV and has a reference angle of π/6? What is the angle measure?
11π/6 330
What is (2π)/3 in degrees?
120
What is 17 degrees in radians?
17π/180
What is π in degrees?
180
What is (3π)/2 in degrees?
270
What radian measure is found in Quadrant II and has a reference angle of π/3? What is the degree measure?
2π/3 120
Reference angle to 210
30
What is π/6 in degrees?
30
What is 2π in degrees?
360
What is a positive radian for (-5π)/4
3π/4
Reference angle to 315
45
What is the reference angle for a 135 degree angle?
45
What is π/4 in degrees?
45
What are all of the angles with arcsin(-√3/2)? Given the restriction: π/2 ≤ Ө ≤ 3π/2
4π/3
What radian measure is found in Quadrant III and has a reference angle of π/3? What is the angle measure?
4π/3 240
What radian measure is found in Quadrant IV and has a reference angle of π/3? What is the angle measure?
5π/3 300
What are all of the angles with arcsec(-√2)? Given the restriction: π ≤ Ө ≤ 2π
5π/4
What are all of the angles with arccos(-√3/2)? Given the restriction: 0 ≤ Ө ≤ π
5π/6
What are all of the angles with arctan(-√3/3)? Given the restriction: π/2 ≤ Ө ≤ 3π/2
5π/6
Reference angle to 120
60
What is the reference angle for a 240 degree angle?
60
What is π/3 in degrees?
60
What is 35 degrees in raidans?
7π/36
What are all of the angles with arcsec(√2)? Given the restriction: π ≤ Ө ≤ 2π
7π/4
What radian measure is found in Quadrant IV and has a reference angle of π/4? What is the degree measure?
7π/4 315
Given two sides (b and c) and an inclusive angle (A), what is the formula to find the Area of the triangle?
A=(bc)/2 * SinA
What is Heron's Area Formula?
A=√(s(s-a)(s-b)(s-c))
What three types of triangles (AAS, SSS, etc.) are used when using the Law of Sines?
AAS, ASA, ASS
What is the reciprocal of Sine?
Cosecant
What is the reciprocal of Tangent?
Cotangent
Are decimals or π terms used when converting radians to degrees?
Decimals (usually π cancels out)
Formula to convert degrees to radians
Degree * (π/180)
What is the arcsin(1.34)?
Not applicable arcsin's cannot be taken of any number greater than 1
What quadrant is (3π)/4 in?
Quadrant II
What quadrant is a 135 degree angle in?
Quadrant II
What quadrant is (3π)/4 in? What's the angle measure?
Quadrant II; 135
What quadrant is a 240 degree angle in?
Quadrant III
What quadrant is (7π)/6 in? What is the angle measure?
Quadrant III 210
What quadrant is (5π)/3 in? What is the angle measure?
Quadrant IV 300
What Quadrants contain Tan(√3)?
Quadrants I and III
What quadrants are Cos(√3/2) in?
Quadrants I and IV
Formula to convert radians to degrees
Radian * (180/π)
What is the reciprocal of Cosine?
Secant
Positive/negative values of Sine, Cosine, and Tangent in Quadrant I
Sine: + Cosine: + Tangent: +
Positive/negative values of Sine, Cosine, and Tangent in Quadrant II
Sine: + Cosine: - Tangent: -
Positive/negative values of Sine, Cosine, and Tangent in Quadrant IV
Sine: - Cosine: + Tangent: -
Positive/negative values of Sine, Cosine, and Tangent in Quadrant III
Sine: - Cosine: - Tangent: +
What are inverse functions used for?
To find the angle measure with a given side length
What is the Ambiguous Case?
What is it called when the exact number of possible triangles that can be formed is unknown in an Acute ASS triangle in which a<b?
What is the formula to find Cosine?
x/r
What is the formula to find Sine?
y/r
What is the formula to find Tangent?
y/x
Are decimals or π terms used when converting degrees to radians?
π terms
Given that Tan(√3) is found in Quadrants I and III, what are all the angles between 0 and 2π that have the same value as Tan(√3)?
π/3 (Quadrant I) 2π/3 Does NOT work because it is in Quadrant II and is therefore negative 4π/3 (Quadrant III) 5π/3 Does NOT work because it is in Quadrant IV and is therefore negative
What is the reference angle for (3π)/4
π/4
What radian measure is found in Quadrant III and has a reference angle of π/4? What is the degree measure?
π/4 225
Given that Cos(√3/2) is found in Quadrants I and IV, what are all the angles between 0 and 2π that have the same value as Cos(√3/2)?
π/6 (Quadrant I) 5π/6 Does NOT work because it is in Quadrant II and is therefore negative 7π/6 Does NOT work because it is in Quadrant III and is therefore negative 11π/6 (Quadrant IV)
Cos(315)
√2/2
Cos(45)
√2/2
Sin(45)
√2/2
What is Sin(135) (given that the reference angle is 45 and the angle is in Quadrant II)?
√2/2
What is Sin[(3π)/4] (given that the reference angle is π/4)?
√2/2
Tan(60)
√3
What is Tan(240) (given that the reference angle is 60 and the angle is in Quadrant III)?
√3
Cos(30)
√3/2
Sin(120)
√3/2
Sin(60)
√3/2
Tan(30)
√3/3
