To verify the expression sin(90°) + cos(θ), we can utilize the sine and cosine values in trigonometry.
First, it’s essential to recall that sin(90°) equals 1. This is a fundamental value in trigonometric functions:
- sin(90°) = 1
Using this, we can rewrite our expression:
sin(90°) + cos(θ) = 1 + cos(θ)
This indicates that the expression will vary based on the value of cos(θ).
However, what we want to achieve is to understand under what circumstances 1 + cos(θ) equals 1. The equation simplifies to:
cos(θ) = 0
Hence, sin(90°) + cos(θ) = 1 when cos(θ) is 0, which happens when θ equals 90° + k·180°, where k is any integer (from periodic properties of cosine). Therefore:
The sum identity, in this case, would typically not apply directly since we aren’t manipulating angles in a sum or difference form. Instead, we are merely evaluating these trigonometric identities at specific angles. For verification:
We can also refer to the Pythagorean identity:
sin²(θ) + cos²(θ) = 1
When θ = 90°, we have:
sin²(90°) + cos²(90°) = 1 + 0 = 1
This confirms that for the specific case of sin(90°) + cos(θ), it holds true under certain conditions. In summary, while there isn’t a direct sum or difference identity to apply here, the evaluation of trigonometric values demonstrates that:
sin(90°) + cos(θ) = 1 + cos(θ) evaluates to 1 under the condition that cos(θ) = 0.