That big ole 3 right in the middle is the constant of proportionality.
For starters,
tan(2θ) = sin(2θ) / cos(2θ)
and we can expand the sine and cosine using the double angle formulas,
sin(2θ) = 2 sin(θ) cos(θ)
cos(2θ) = 1 - 2sin^2(θ)
To find sin(2θ), use the Pythagorean identity to compute cos(θ). With θ between 0 and π/2, we know cos(θ) > 0, so
cos^2(θ) + sin^2(θ) = 1
==> cos(θ) = √(1 - sin^2(θ)) = 4/5
We already know sin(θ), so we can plug everything in:
sin(2θ) = 2 * 3/5 * 4/5 = 24/25
cos(2θ) = 1 - 2 * (3/5)^2 = 7/25
==> tan(2θ) = (24/25) / (7/25) = 24/7
Answer:
16. -7x-14
17. -20+5y
18. -8b+8
19. -16c-12
20. 5w+40
21. -12x+6
22. 2z-4
23. -28p-28
24. -9t+54
25. Can't tell what this problem is. The picture cuts out.
26. -27+21p
27. 9k-27
28. -7b+9
29. 30t+12
30. 7v-28
Step-by-step explanation:
Answer:
x = 27, y = 74
Step-by-step explanation:
Hi again :)
Since the angles of 5x + 4 and the one adjacent to x = 14 are corresponding angles, they are equal. That means that (5x + 4) + (x + 14) = 180 degrees.
5x + 4 + x + 14 = 180
6x + 18 = 180
6x = 162
x = 27
Also, the angle (5x + 4) and (2y - 9) are vertical angles, they are equal in value. We know the value of x now, so we'll substitute that in and solve for y.
5(27) + 4 = 2y - 9
135 + 4 = 2y - 9
139 = 2y - 9
148 = 2y
y = 74
As always, lmk if you have questions.
Answer: A=5/7. B=3/2. C=1/6
D=3/5. E=14/11. G=5/7 H=3/2 I=1/6 j=3/5 K=14/11 L=7/8
Step-by-step explanation:
