sin(-π) + cos 5π

how to solve without a calculator.
Please write steps and explain

thank you

answer is -1

Answer is -1

To solve the expression without a calculator, let's start by evaluating the individual trigonometric functions and then substitute the values into the given expression.

1. Evaluating sin(-π):
The sine function is periodic with a period of 2π. Since -π is equivalent to π radians, we know that sin(-π) is equal to sin(π). The sine function is negative in the third and fourth quadrants, and in both quadrants, it has the same absolute value. Thus, sin(π) = -sin(0) = 0.

2. Evaluating cos(5π):
Similar to the sine function, the cosine function is periodic with a period of 2π. Since 5π is equivalent to π radians, we can rewrite cos(5π) as cos(π). The cosine function is negative in the second and third quadrants, and in both quadrants, it has the same absolute value. Therefore, cos(π) = -cos(0) = -1.

Now, substitute the evaluated values back into the original expression:

sin(-π) + cos(5π) = 0 + (-1) = -1.

Hence, the final answer to the expression sin(-π) + cos(5π) without a calculator is -1.