# Thread:

1. ## Sign of sine in 3d rotation

(x,y,z) and (X,Y,Z) are two unit vectors. Both are perpendicular to a unit vector (u,v,w) and -1 < Y < 1.

Is there any simple method to determine the sign of $sin(\theta)$ (theta is angle for rotating X,Y,Z about u,v,w into x,y,z). When I solve the equations for rotating (X,Y,Z) about (u,v,w), i always get possible null-division, so I need two conditional expressions. Couldn't there be a simpler method like the sign of a projection or something like that?

2. ## Re: Sign of sine in 3d rotation

The scalar product of (x,y,z) and (X,Y,Z) gets you the cosine of the angle between them doesn't it ? From that you can deduce the sine.
Or am I misreading the question ?
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.8879801034927368, "perplexity_flag": "middle"}