I'm not sure how to solve these with calculator.
sec x = -2 , π ≤ x ≤ 3π
sinθ=0.1473, 0°≤θ≤90°
cosθ=0.7563, 0°≤θ≤90°
To solve these equations with a calculator, you'll need to use the trigonometric functions present on most scientific calculators. Here's how you can find the solutions:
1. sec x = -2, π ≤ x ≤ 3π:
- Start by finding the cosine of x using the inverse of the secant function: cos x = 1/sec x = -1/2.
- Take the inverse cosine (cos^(-1)) of -1/2, which will give you the angle in radians between 0 and π. Let's call this angle A.
- Since the given range is π ≤ x ≤ 3π, add 2π to the value of A to get one solution in this range. This is your first solution, x1.
- To find the second solution, subtract 2π from the value of A. This will give you a solution in the specified range by the question, which is your second solution, x2.
2. sinθ = 0.1473, 0° ≤ θ ≤ 90°:
- Take the inverse sine (sin^(-1)) of 0.1473, which will give you an angle in degrees between 0 and 90. Let's call this angle B.
- This is your solution, θ = B.
3. cosθ = 0.7563, 0° ≤ θ ≤ 90°:
- Take the inverse cosine (cos^(-1)) of 0.7563, which will give you an angle in degrees between 0 and 90. Let's call this angle C.
- This is your solution, θ = C.
By following these steps and using the trigonometric functions on your calculator, you'll be able to find the solutions to these equations.