Show that Cos(arcsin z) 1. Notes: 1. Cannot use derivative. 2. Work from one side to transform to the other side. 3. Use a right triangle and the definitions of trig functions. Do work on a piece of paper.

sol only thank you.

Find the slope of the tangent line to the sine function at the origin. y 2 y= sin(7 x) 1 Compare these values with the number of complete cycles in the interval [0, 2n]. O The slope is half the the number of cycles in the interval. O The slope is twice the number of cycles in the interval. O There is no relationship between slope and number of cycles. O The slope squared gives the number of cycles in the interval. O The slope is equal to the number of cycles in the interval.

9. Fill in the blanks AND give reasons for each step of the calculation. Let y = arctan(r+ e). (This could also be written y = tan- (r + e).) We will find its derivative. First rewrite the equation as tan( using the definition of Now apply the method of to get 윤 tan( On the left side of the equation we use the to get: sec ( Now we solve for to get = This shows that arctan(r+ e") %3D If we want to, we can use trigonometry to write the final answer using only the variable r, but for simplicity we'll leave the answer as it is.