Find the sine, cosine and tangent of the angle BOP if O is the origin and points B (1; 0)

Find the sine, cosine and tangent of the angle BOP if O is the origin and points B (1; 0) and P (-3/4: y) lie on the unit semicircle.

The scalar product of two vectors is a number equal to the sum of the products of their respective coordinates.
For vectors OB and OP, the dot product will be expressed by the formula:
-3/4 1 + 0 y = – 3/4;
These vectors are unit, since they are the radii of the unit circle and have a modulus equal to one.
The scalar product of two vectors is the number equal to the product of the lengths of these vectors by the cosine of the angle between them.
Then:
| ОВ | · | OP | Cosα = -3/4;
cosα = -3/4;
The sine α is determined from the relation: sin ^ 2 (α) + cos ^ 2 (α) = 1; α Є (0; π)
sin ^ 2 (α) = 1 – 9/16 = 7/16;
sinα = √7 / 4;
tgα = sinα / cosα = √7 / 4: (-3/4) = – √7 / 3;
Answer: √7 / 4; – 3/4; – √7 / 3;