<P> Again, in solving the tan (h) equation for h, use of the two - argument arctangent that accounts for the quadrant is recommended . Thus, again consistent with the convention of azimuth being measured from the south and opening positive to the west, </P> <Dl> <Dd> h = arctan ⁡ (x, y) (\ displaystyle h = \ arctan (x, y)), </Dd> </Dl> <Dd> h = arctan ⁡ (x, y) (\ displaystyle h = \ arctan (x, y)), </Dd> <Dl> <Dd> x = sin ⁡ (φ o) cos ⁡ (a) cos ⁡ (A) + cos ⁡ (φ o) sin ⁡ (a) y = cos ⁡ (a) sin ⁡ (A) (cos ⁡ (δ) cos ⁡ (h) cos ⁡ (δ) sin ⁡ (h) sin ⁡ (δ)) = (sin ⁡ (φ o) 0 cos ⁡ (φ o) 0 1 0 − cos ⁡ (φ o) 0 sin ⁡ (φ o)) (cos ⁡ (a) cos ⁡ (A) cos ⁡ (a) sin ⁡ (A) sin ⁡ (a)) (cos ⁡ (δ) cos ⁡ (α) cos ⁡ (δ) sin ⁡ (α) sin ⁡ (δ)) = (cos ⁡ (θ L) sin ⁡ (θ L) 0 sin ⁡ (θ L) − cos ⁡ (θ L) 0 0 0 1) (sin ⁡ (φ o) 0 cos ⁡ (φ o) 0 1 0 − cos ⁡ (φ o) 0 sin ⁡ (φ o)) (cos ⁡ (a) cos ⁡ (A) cos ⁡ (a) sin ⁡ (A) sin ⁡ (a)). (\ displaystyle (\ begin (aligned) x& = \ sin \ left (\ phi _ (\ text (o)) \ right) \ cos \ left (a \ right) \ cos \ left (A \ right) + \ cos \ left (\ phi _ (\ text (o)) \ right) \ sin \ left (a \ right) \ \ y& = \ cos \ left (a \ right) \ sin \ left (A \ right) \ \ (3pt) (\ begin (bmatrix) \ cos \ left (\ delta \ right) \ cos \ left (h \ right) \ \ \ cos \ left (\ delta \ right) \ sin \ left (h \ right) \ \ \ sin \ left (\ delta \ right) \ end (bmatrix)) & = (\ begin (bmatrix) \ sin \ left (\ phi _ (\ text (o)) \ right) &0& \ cos \ left (\ phi _ (\ text (o)) \ right) \ \ 0&1&0 \ \ - \ cos \ left (\ phi _ (\ text (o)) \ right) &0& \ sin \ left (\ phi _ (\ text (o)) \ right) \ end (bmatrix)) (\ begin (bmatrix) \ cos \ left (a \ right) \ cos \ left (A \ right) \ \ \ cos \ left (a \ right) \ sin \ left (A \ right) \ \ \ sin \ left (a \ right) \ end (bmatrix)) \ \ (\ begin (bmatrix) \ cos \ left (\ delta \ right) \ cos \ left (\ alpha \ right) \ \ \ cos \ left (\ delta \ right) \ sin \ left (\ alpha \ right) \ \ \ sin \ left (\ delta \ right) \ end (bmatrix)) & = (\ begin (bmatrix) \ cos \ left (\ theta _ (L) \ right) & \ sin \ left (\ theta _ (L) \ right) &0 \ \ \ sin \ left (\ theta _ (L) \ right) & - \ cos \ left (\ theta _ (L) \ right) &0 \ \ 0&0&1 \ end (bmatrix)) (\ begin (bmatrix) \ sin \ left (\ phi _ (\ text (o)) \ right) &0& \ cos \ left (\ phi _ (\ text (o)) \ right) \ \ 0&1&0 \ \ - \ cos \ left (\ phi _ (\ text (o)) \ right) &0& \ sin \ left (\ phi _ (\ text (o)) \ right) \ end (bmatrix)) (\ begin (bmatrix) \ cos \ left (a \ right) \ cos \ left (A \ right) \ \ \ cos \ left (a \ right) \ sin \ left (A \ right) \ \ \ sin \ left (a \ right) \ end (bmatrix)). \ end (aligned))) </Dd> </Dl>

A coordinate used to define the position of sun moon or star