Use a half-angle identity to find the exact value of tan(5\pi )/(12)
1 answer:
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Answer:
9. 66°
10. 44°
11.
12.
13. 27.3
14. 33.9
15. 22°
16. 24°
Step-by-step explanation:
9. Add 120 + 80 (equals 200) and subtract that from 360 (Because all angles in a quadrilteral add to 360°), this equals 160. Plug the same number in for both variables in the two other angle equations until the two angles add to 160. For shown work on #9, write:
120 + 80 = 200
360 - 200 = 160
12(5) + 6 = 66°
19(5) - 1 = 94°
94 + 66 = 160
10. Because the two sides are marked as congruent, the two angles are as well. This means the unlabeled angle is also 68°. The interior angles of a triangle always add to 180°, so add 68+68 (equals 136) and subtract that from 180, this equals 44. For shown work on #10, write:
68 x 2 = 136
180 - 136 = 44
11. Use the Pythagorean theorem (a² + b² = c²) (Make sure to plug in the hypotenuse for c). Solve the equation. For shown work on #10, write:
a² + b² = c²
a² + 6² = 8²
a² + 36 = 64
a² = 28
a =
a =
12. (Same steps as #11) Use the Pythagorean theorem (a² + b² = c²) (Make sure to plug in the hypotenuse for c). Solve the equation. For shown work on #11, write:
a² + b² = c²
a² + 2² = 4²
a² + 4 = 16
a² = 12
a =
a =
13. Use SOH CAH TOA and solve with a scientific calculator. For shown work on #13, write:
Sin(47°) =
x = 27.3
14. Use SOH CAH TOA and solve with a scientific calculator. For shown work on #14, write:
Tan(62°) =
x = 33.9
15. Use SOH CAH TOA and solve with a scientific calculator. For shown work on #15, write:
cos(θ) = 52/56
θ = cos^-1 (0.93)
θ = 22°
16. (Same steps as #15) Use SOH CAH TOA and solve with a scientific calculator. For shown work on #16, write:
sin(θ) = 4/10
θ = sin^-1 (0.4)
θ = 24°
Good luck!!