Help on this ACT Math question?

Test Preparation
1

I was going over my incorrect answers on an ACT math section from the ACT Online Prep, and I couldn’t really understand this question:

Given that 2sina = 2 and 2cos(π2 − b) = 2, which of the following could be a value, in radians, of a + b?

A. 0
B. π2
C. 2
D. π
E. 2π

2

Sorry B. is π/2, by the way

3

bump

4

@avu017 this is basically two separate problems, solve for a and b:

2 sin a = 2 <==> sin a = 1 <==> a = pi/2 + (2k*pi) where k is an integer (to solve quickly, look at the unit circle and note that sin(pi/2) = 1. You can add any multiple of 2pi and the sine of that angle will still be 1).

2 cos (pi/2 - b) = 2 <==> cos (pi/2 - b) = 1 <==> b = pi/2 + (2m*pi) where m is an integer

Adding the two solutions, we have a+b = pi + (2(k+m)*pi) where k and m are integers, and only D) is a possible value.

5

Thanks @MITer94 that was really helpful!