To evaluate the expression 1 – sin x, we start by understanding what it means in the context of trigonometry. The sine function, sin x, represents the ratio of the opposite side to the hypotenuse in a right triangle for a given angle x.
So, when you see 1 – sin x, it signifies that you take the value of the sine function at angle x and subtract it from 1. The value of sin x varies between -1 and 1, depending on the angle x. Consequently, 1 – sin x can range from 0 to 2. Specifically:
- If sin x = 0, then 1 – sin x = 1.
- If sin x = 1, then 1 – sin x = 0.
- If sin x = -1, then 1 – sin x = 2.
This expression can be useful in various mathematical contexts, such as solving equations, analyzing graphs, or simplifying expressions. To find a numerical value for 1 – sin x, you would need a specific angle x. For example, if x = 30°, then:
1 – sin 30° = 1 – 0.5 = 0.5.
In conclusion, evaluating 1 – sin x involves substituting a specific angle into the sine function and performing a simple subtraction to find the result.