Question

Cos(-105°)+sin(-915°)

Answer 1

Cos(-105)=cos(-90-45)=sin-45
sin(-915)=sin(-195)=sin(-180-15)=sin-15
-sin45-sin15=-2sin45-15\2cos45+15\2=
=-2sin15cos30=-2√2\2sin15=-√2sin15

Answer 2

To evaluate the expression cos(-105°) + sin(-915°), let's first simplify each trigonometric function separately:

cos(-105°): The cosine function has a periodicity of 360 degrees, meaning that cos(x) = cos(x + 360°) for any angle x. Therefore, we can find the equivalent angle within one period.

-105° + 360° = 255°

Now, we can evaluate cos(255°). However, note that the cosine function is an even function, which means cos(-x) = cos(x). Hence, cos(255°) = cos(-105°).

sin(-915°): Similarly, the sine function has a periodicity of 360 degrees, so we can find the equivalent angle within one period.

-915° + 360° = -555°

Again, the sine function is an odd function, meaning sin(-x) = -sin(x). Thus, sin(-915°) = -sin(555°).

Now, let's calculate the values:

cos(-105°) = cos(255°) ≈ 0.9659 (rounded to four decimal places) sin(-915°) = -sin(555°) ≈ -0.8240 (rounded to four decimal places)

Finally, we can substitute these values back into the original expression:

cos(-105°) + sin(-915°) ≈ 0.9659 + (-0.8240) ≈ 0.1419 (rounded to four decimal places)

Therefore, cos(-105°) + sin(-915°) is approximately 0.1419.