Solve sin θ = 0.95 for -90º ≤ θ ≤ 90º. Round to the nearest tenth.

Start drawing these things on paper.

-90 to + 90 is in quadrants 4 to 1
in quadrant 4 the sin of theta is negative, y is down and x is right.
Therefore this is really only from
0º ≤ θ ≤ 90º
sin^-1 0.95 = 71.8 degrees

Thank you so much!

To solve the equation sin θ = 0.95 for -90º ≤ θ ≤ 90º and round to the nearest tenth, we can use inverse sine (also known as arcsine) function. The inverse sine function calculates the angle whose sine is a given value.

In this case, we want to find the angle θ whose sine is 0.95. To do that, follow these steps:

1. Input the value into the inverse sine function: sin^(-1)(0.95).
2. Use a scientific calculator or a trigonometric table to find the value of sin^(-1)(0.95).

Using a scientific calculator, the inverse sine of 0.95 is equal to approximately 73.7 degrees.

Now, since we are looking for an angle within the range of -90º to 90º, there are two possible angles. One is positive and the other is negative.

The positive angle within the given range is 73.7 degrees (rounded to the nearest tenth).

Therefore, the solution to sin θ = 0.95 for -90º ≤ θ ≤ 90º is approximately θ = 73.7 degrees.