Answer:
θ = 60° or θ = 120°, which in radians is equivalent to θ = π/3 rad or θ = 2π/3 rad.
Explanation:
The given equation is sin θ = (√3)/2
Solving that equation is finding the value of the angle, θ, whose sine is (√3)/2.
The function that returns the value of the angle whose sine is (√3)/2 is the inverse function of the sine and it has a special name: arc sine or arcsin.
Hence, θ = arcsin (√3)/2.
You can use your knowledge of the notable angles to solve for that equation.
1) The function sine is positive in first and second quadrants.
2) The angles in the first quadrant go from 0° to 90°.
3) The sine of 60° (√3)/2, Hence the first value of θ is 60°
4) The angles in the second quatrant go from 90° to 120°. 60° is the reference angle in the second quadrant, and the angle searched is
- 180° - reference angle = 180° - 60° = 120°. So, 120° is the other solution of the equation.
5) You can convert both angles to radians using the equivalence
- π radians = 180° ⇒ 1 = π rad / 180°
- 60° = 60° × π rad / 180° = π/ 3 rad
- 120° = 120° × π rad / 180° = 2π/3 rad
6) You can verify that sin 60° = (√3)/2 = sin 120° .
Answer:
h=−6, k=−30
Step-by-step explanation:
did on edge
Change the mixed fractions to an improper fraction.
4 5/7 = 32/7
1 6/7 = 13/7
Now you can easily subtract since both fractions have common denominators
32/7 - 13/7
(Think: 32 - 13 = 19)
Change the improper fraction to a mixed fraction
19/7 = 2 5/7
Answer: 2 5/7
Hope I helped =)
Answer:
Step-by-step explanation:
2. 2c(7c + 1)
3. stays as is
4. 2x^3y^4(4 - 11x^2y^2)
5. ab(10ab + 9b - a)
6. 3m^2(7m^4n^2+2m^2n+5)
7. (a - 8)(a + 8)
8. (y - 17)(y + 17)
9. stays as is
10. (1 - 5n)(1 + 5n)
11. (4x - 7y)(4x + 7y)
12. (w^2 - 10)(w^2 + 10)
13. (c - 9d)(c + 9d)
14. (14a - b)(14a + b)
Answer:
I believe the answers are a and e.
Step-by-step explanation:
Let me know if you want an explanation.
Hope this helps!!!
