# Thread: Trig Functions (Angles subtended?)

1. ## Trig Functions (Angles subtended?)

Done

2. Originally Posted by MathIsPower
Hey everyone I really need help with this question for my homework and I'm having a hard time with it.

Q- The angle subtended at the center by the arc PQ is 3Pi/8 radians. R is the midpoint of arc PQ. Find the shaded area.

http://olympic.txc.net.au/AK/help.JPG (Diagram)

Hello,

the shaded area can be calculated by:

area of sector - area of right triangle

The angle(ROP) = $\displaystyle \frac{3 \pi}{16}$

Thus the area of the sector is: $\displaystyle \frac{A_{sector}}{\pi r^2}=\frac{\frac{3 \pi}{16}}{2\pi} \ \Longleftrightarrow \ A_{sector}=\frac{3}{32} \pi r^2$

The area of the right triangle is $\displaystyle A_{\text{right triangle}}=\frac{1}{2} \cdot {base} \cdot {height}$

If r is the length of the radius (here r = 4 cm) then the length of the base:$\displaystyle b=r \cdot \cos \left(\frac{3 \pi}{16} \right)$ and

the length of the height is: $\displaystyle h=r \cdot \sin \left(\frac{3 \pi}{16} \right)$

$\displaystyle A_{\text{shaded area}}=\frac{3}{32} \pi r^2 - \frac{1}{2} \cdot r \cdot \cos \left(\frac{3 \pi}{16} \right) \cdot r \cdot \sin \left(\frac{3 \pi}{16} \right)$