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° .
x-(3x+4)=34
x= -19
-19-(3(-19)+4)=34
-19+(57-4)=34
-19+(53)=34
-19+53=34
34=34
therefore the first number is -19 and the second number is 53
Answer:
C.)9
Step-by-step explanation:
You add up all your data to get 54 and divide by the amount of numbers you had in the data which was 6. So if you divide 54 by 6 you get 9.
The answer is the second option.
To find the answer quickly, fist look at the signs associated with the terms. The is a negative sign with the B and C in the original equation, and the second option is the only one that follows that.
You use 6 as the C since that is a shared value when multiplying 2 and 3, so 1/2 becomes 2 and 1/3 becomes 3.
