Co-interior properties. 180 degrees = two co-interior angles.
180 = (2y+50) + (3y+40)
180 = 5y + 90
90 = 5y
/5 /5
18 = y
Angle 1: 2y + 50
2(18) + 50
36 + 50
86
Angle 2: 3y + 40
3(18) + 40
54 + 40
94
86 + 94 = 180 so it is true.
Now the sides.
On a parallelogram, 5x+2 and 8x-7 must be equal
5x + 2 = 8x - 7
2 = 3x - 7
9 = 3x
/3 /3
3 = x
Side 1: 5x + 2
5(3) + 2
15 + 2
17
Side 2: 8x - 7
8(3) - 7
24 - 7
17
Both sides are equal; 17.
Angle 1: 86
Angle 2: 94
Sides: 17
The answer to this problem is false.
Answer:
- sin(θ) = -(4√15)/17
- cos(θ) = 7/17 . . . . . . . given
- tan(θ) = -(4√15)/7
- csc(θ) = -(17√15)/60
- sec(θ) = 17/7
- cot(θ) = -(7√15)/60
Step-by-step explanation:
The relationship between sine and cosine is ...
sin² + cos² = 1
Solving for sine gives ...
sin = ±√(1 -cos²)
In this problem, we want the negative root.
sin(θ) = -√(1 -(7/17)²) = -√(240/289) = -(4√15)/17
tan(θ) = sin(θ)/cos(θ) = ((-4√15)/17)/(7/17) = -(4√15)/7
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And the inverse functions are ...
sec(θ) = 1/cos(θ) = 17/7
csc(θ) = 1/sin(θ) = -17/(4√15) = -(17√15)/60
cot(θ) = 1/tan(θ) = -(7√15)/60
_____
Of course, you're aware that 1/√15 = (√15)/15.
is acute, then slope is positive;