Find exactly cos 150˚ + sin 225˚?

Question

Find exactly cos 150˚ + sin 225˚

Answer 1

cos 150˚ + sin 225˚

= cos (180˚ - 30˚) + sin (180˚ + 45˚)

= -cos30˚ - sin45˚

= -√3/2 - 1/√2

= -√3/2 - √2/2

= -½(√3 +√2)

Answer 2

cos 150=-cos 30=-√3/2 sin 225=-sin 45=-√2/2 cos 150+sin 225=-(√3+√2)/2

Answer 3

These are basic trigonemtric relationships that you'll need to know on your own for future work. cos(150) + sin(225) = cos(180 - 30) + sin(180 + 45) = -cos(30) - sin(45) = -sqrt(3)/2 - 1/sqrt(2) = (-sqrt(3) - sqrt(2))/2.

You should memorize sin, cos, and tan for the following angles in the first quadrant: 0, 30, 45, 60, 90. sin, cos, and tan are all positive or zero in the first quadrant (but tan is undefined at 90). Then, for angles in other quadrants, you just need to see what the angle is to the x-axis and determine if sin (tied to y) and cos (tied to x) are positive or negative.

Answer 4

-0.064319171500008189078200952197586