Question
The point P=(20,-15) on the circle x^2+y^2=r^2 Is also on the terminal side of an angle B in standard position. Find sinTheta ,cosTheta ,tanTheta ,cscTheta sinTheta = (Type an integer or a simplified fraction.) cosTheta =square (Type an integer or a simplifed fraction.) tanTheta =square (Type an integer or a simplifee fraction.) cscTheta =square (lype an integer or a simplifed fraction) secTheta =square (Iype an integer or a simplifeed fraction.) cotTheta =square (Type aninteger or a simplifee fraction.)
Solution
4.5
(262 Votos)
Ricardo
Elite · Tutor por 8 anos
Resposta
To find the trigonometric functions of angle
where point
lies on the terminal side of
, we first need to find the radius
of the circle using the Pythagorean theorem, since
is on the circle
. The radius
is the distance from the origin to point
, which is the hypotenuse of a right triangle with legs of lengths 20 and 15.Using the Pythagorean theorem:
Now, we can find the trigonometric functions:1. **Sine (
)**:
2. **Cosine (
)**:
3. **Tangent (
)**:
4. **Cosecant (
)**:
5. **Secant (
)**:
6. **Cotangent (
)**:
So, the values are: