Please help with 1215 Thanks Student Number Label each of t

Please help with 12-15. Thanks
.

Student Number Label each of the following statements as true or false. If false, replace the underlined word(s) or expression to produce a true statement. 12. On the interval- , the only intersection point of the graphs of y and y = sin is at =0. 13. The graph of y cos( +-) is a reflection of the graph ofv-sine in the x-axis. 3T The function y = 7 sin |2x | is even the values of sin and cos , and prove that sin2 + cos2 = 1 15. Given the right triangle AABC as shown, fill in cos = sin =

Solution

12) False .

since y = intersects y = sin at one point or two points or they does not intersect at all based on value of .

13) y = cos( + /2) = -sin

False since y = cos( + /2) and y = -sin are both same.

14) A function is even when x is replaced by -x , and the value of function does not change

Here the value of function changes when x is replaced by -x . Hence False

15) sin = opposite side / hypotenuse = a/c

cos = adjacent side / hypotenuse = b/c

from pythagorous theorem a² + b² = c²

sin² + cos² = (a/c)² + (b/c)²

==> (a² + b²)/c² = c²/c² = 1

Hence sin² + cos² = 1