## anonymous 5 years ago Use the fact that the trig functions are periodic to find the exact value of the given expression. sin ((17pi)/4) = ((sqrt{2})/2)

1. anonymous

2. Mertsj

yes

3. Mertsj

17pi/4 is the same as pi/4

4. anonymous

To clarify, the value of sin(17pi/4) is the same as sin(pi/4) ;) pi/4 radians is 45 degrees. Take a triangle ABC with A at the origin, B at (1,0), and C at (1,1). You'll have a right angle at B and 45 degree angles at A and C. AC will have a 45 degree angle over the x-axis. sin is the same as the ratio BC/AC. You know AB and BC are both 1 units long. Pythagoras knew that AB^2+BC^2 = AC^2, which in our case is 1^2+1^2 = AC^2, so AC = sqrt(2); since we know BC/AC is the same as sin(pi/4) (because AC's angle over the x axis is pi/4), it follows that BC/AC = sin(pi/4), or sin(pi/4) = 1/sqrt(2), which is sqrt(2)/2 :)

5. myininaya

17pi/4 is not the same as pi/4 but sin(17pi/4) is the same as sin(pi/4) since $\sin(\frac{16}{4} \pi +\frac{1 }{4 }\pi)=\sin(2\pi+\frac{\pi}{4})=\sin(\frac{\pi}{4}) \text{ since twopi is just one rotation }$

6. anonymous

For what numbers theta is f(theta)=tan(theta) not defined? f(theta)=tan(theta) is not defined for numbers that are (even multiples, odd multiples, multiples) of (45*, 90*, 180*). Select an answer from each set of parentheses.