Solve the equation sinθ=0.3 to the nearest tenth. Use the restrictions 90°≤θ≤180°.
To solve the equation sinθ=0.3 in the given range of 90°≤θ≤180°, we can use the inverse sine function or arcsine function.
1. Calculate the inverse sine of 0.3 using a calculator:
sin^(-1)(0.3) ≈ 17.5°
2. Since the given range for θ is 90°≤θ≤180°, we need to find the angle θ within this range whose sine is approximately 0.3.
3. Subtract the calculated angle from 180° to find the angle in the range:
180° - 17.5° ≈ 162.5°
Thus, the solution to the equation sinθ=0.3 in the range 90°≤θ≤180° is θ ≈ 162.5° (to the nearest tenth).
To solve the equation sinθ = 0.3, we need to find the angle θ within the restricted range of 90° to 180° that satisfies this equation.
Since sine is a periodic function, it repeats its values after every 360 degrees. Therefore, we can find the solution in the first 360-degree interval and then adjust it to fit within the restricted range.
To find the angle θ in the first 360-degree interval, we can use the inverse sine function (sin⁻¹) or arcsin on both sides of the equation:
θ = sin⁻¹(0.3)
Using a calculator, find the inverse sine (arcsin) of 0.3, which is approximately 17.45°.
However, we need to ensure that the solution is within the restricted range of 90° to 180°. Let's check if 17.45° satisfies this criterion.
Since 17.45° is less than 90°, it does not fit within the restricted range. This means we need to find the next solution within the first 360-degree interval.
To do that, we can subtract 17.45° from 180° to get the next solution:
180° - 17.45° ≈ 162.55°
Now, we have found an angle, approximately 162.55°, which satisfies the equation sinθ = 0.3 within the restricted range of 90° to 180°.
Therefore, the solution to the equation sinθ = 0.3 to the nearest tenth within the given restrictions is θ ≈ 162.6°.
Can you use tables, a calculator or a power series?
The answer is 162.5 degrees.
17.46 degrees (0.3047 radians) has the same sine, and one could use the expansion
sin x = x - x^3/6 + x^5/120 +...
to show that sin 0.3047 = 0.3