Probabilty help! I keep getting the wrong answer?

Question

1. A continuous randon variable X has a probabilty density function given by:

(1/2)sinX, if 0 0, elsewhere

The value of 'a' such that Pr(X.a)=0.25 is?
a) 0.25
b) 0.75
c) 1.04
d) 1.05
e) 2.09

Please show working, I don't know what I'm doing wrong. Thanks!

Answer 1

if Pr(X) = 1/2*sin X = 0.25
then sin X = 0.5

In the interval 0 < X < Pi :
Sin X = 0.5 means X = 1/3.Pi
That's equal to 1.047197551

Closest answer is d)

Answer 2

The values of 'a' such that Pr(X,a) = 0.25 are: pi/6 and 5pi/6

SinX >0 on the interval 0 1/2 SinX = 0.25 when SinX = 0.5
This is true if X = pi/6 or X = 5pi/6

Answer 3

1/2 sinx = 1/4
sinx = 1/2
x = 3.14/6 or 5*3.14/6
= 0.52 or 2.6

Answer 4

.........a..... ..... ..... ..... ..... a
(1/2)∫sinXdX = -(1/2)cosX | = (cos(0) - cos(a))/2
........0..... ..... ..... ..... ..... .0

(1 - cos(a))/2 = 0.25
cos(a) = 0.5
a = π/3 = 1.047
P(0 ≤ X ≤ a) ≈ 1.047