Question

What is the y-value of the point of intersection of y=2sinx-cosx and y=cosx over the interval 0≤x≤pi/2 ? a. 0 b. (square root of 2)/2 c. (square root of 3)/2 d. 1

Answer 1

Option b. √2/2 is the correct option.

Explanation:

Two functions are given as y = 2sinx - cosx and y = cosx

Now we have to find the point of intersection of two given functions.

So at the point of intersection of these graphs

2 sinx - cosx = cosx

2 sinx = 2 cosx

sinx = cosx

For the given value of x = π/4 sine and cosine functions are equal.

Therefore y value of both the functions

y = cos(π/4) = 1/√2 = √2/2

Therefore over the interval 0≤x≤π/2 value of y coordinate will be √2/2.

Answer 2

we have that

y=2sinx-cosx
y=cosx
over the interval 0≤x≤pi/2-------> 0≤x≤1.57

using a graph tool
see the attached figure

the solution in the given interval is the point (pi/4, 0.707)
the y-value of the point of intersection is 0.707 -----> √2/2

the answer is the option
b. (square root of 2)/2