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Help on this ACT Math question?

avu017avu017 32 replies7 threads Junior Member
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

4 replies
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Replies to: Help on this ACT Math question?

  • avu017avu017 32 replies7 threads Junior Member
    Sorry B. is π/2, by the way
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  • avu017avu017 32 replies7 threads Junior Member
    bump
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  • MITer94MITer94 4728 replies19 threads Senior Member
    edited August 2016
    @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.
    edited August 2016
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  • avu017avu017 32 replies7 threads Junior Member
    Thanks @MITer94 that was really helpful!
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