15 andtana 3 If sin 0 the sina Note sin x y sin x cos

-15 and(tana ) =? 3. If sin = > 0, the sin(a + (Note: sin (x + y) = sin x cos y + cos x sin y)

Solution

sin alpha =-1/sqrt5, tan alpha >0 means alpha is in third quadrant

here opposite=1, hypotenuse=sqrt5

adjacet =sqrt(5-1)=2

cos alpha =adjacent/hypotenuse=-2/sqrt5

sin(alpha +pi/4) =sin alpha cos pi/4 +cos alpha sin pi/4

                     =(-1/sqrt5)(sqrt2/2)+(-2/sqrt5)(sqrt2/2) =-3sqrt2/2sqrt5 =-3sqrt10/10

4. cot theta=3/2

adjacent =3 , opposite=2

hypotenuse=sqrt(9+4) =sqrt13

sin theta =opposite/hypotenuse=2/sqrt13

sin²theta =(2/sqrt13)²=4/13