Which of the following values of x is a solution to the equationsin x+cos x=1? Hint: Think about the graphs of sine and cosine separately.
options:
x=45°
x=90°
x=135°
x=180°
1+0 = 1
so, what do you think?
To find the values of x that satisfy the equation x + cos(x) = 1, we can plot the graphs of x and cos(x) separately to observe their intersections.
Let's analyze the given options one by one:
1. x = 45°:
When x = 45°, the equation becomes 45° + cos(45°) = 1. Evaluating this expression, we get 45° + 0.707 ≈ 45.707. Since this value is not equal to 1, it is not a solution.
2. x = 90°:
When x = 90°, the equation becomes 90° + cos(90°) = 1. Evaluating this expression, we get 90° - 0 ≈ 90. Since this value is not equal to 1, it is not a solution.
3. x = 135°:
When x = 135°, the equation becomes 135° + cos(135°) = 1. Evaluating this expression, we get 135° - 0.707 ≈ 134.293. Since this value is not equal to 1, it is not a solution.
4. x = 180°:
When x = 180°, the equation becomes 180° + cos(180°) = 1. Evaluating this expression, we get 180° + (-1) = -1, which is not equal to 1. Therefore, x = 180° is also not a solution.
Hence, none of the given options satisfies the equation x + cos(x) = 1.