How do you find the exact value of sin(-105) degrees without a calculator

Answer 1

-105º is a 75º reference angle in Quadrant III

75º = 45º + 30º

using the trig identity ... sin(α + β) = sin(α) cos(β) + cos(α) sin(β)

Answer 2

I'm sorry I'm stupid could you please simplify that, where would the 45 and 30 go? Thank you for your help

Answer 3

What R_scott is implying is

sin(-105°)
= sin(255°) , -105° and 255 are coterminal angles
= - sin 75°
= - sin(45 + 30)
= - (sin45 cos30 + cos45 sin30)

we both would assume that you know the exact value of these standard angles

Answer 4

sin75º = sin(45º + 30º)
= sin45º cos30º + cos45º sin30º
= √2/2 * √3/2 + √2/2 * 1/2
= √6/4 + √2/4
= √2/4 (√3 + 1)
Now use your reference angle of 75º in QIII and you have
sin -105º = -sin75º