Answer: -45° = -(π/4)
Step-by-step explanation:
sin x + cos x = 0
sinx = -cos x subtracted cos x from both sides
[tex]\dfrac{sin\ x}{cos\ x}=-1[/tex] divided cos x from both sides
tan x = -1 simplified fraction
tan⁻¹ (tan x) = tan⁻¹ (-1) applied inverse tan to both sides
x = tan⁻¹ (-1) simplified
x = -45°
Easier method:
sin x = -cos x
At which points are cos x and sin x opposites?
- In Quadrant II at 135°
- In Quadrant IV at 315 (which equals -45°)
Inverse tan is only valid in Quadrants IV and I so the answer is -45°
