Trigonometry

If sinA=3/5 and cosB=5/13 and if A and B are measures of two angles in Quadrant I, find the exact value of the following functions.

cotB =

sin2A=

3)cos(5pi/6 + B) =

tan(A - pi/4) =

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  1. draw your triangles. These are two of the simplest standard integer-sided ones. The have sides
    3-4-5 and 5-12-13
    So, if
    sinA = 3/5, cosA = 4/5
    cosB = 5/13, sinB = 12/13
    Now just use your definitions and formulas:
    cotB = cosB/sinB = 5/12
    sin2A = 2sinAcosA = 2(3/5)(4/5) = 24/25

    cos(5π/6+B) = cos(5π/6)cosB - sin(5π/6)sinB
    = (-√3/2)(5/13)-(1/2)(12/13)
    = -(12+5√3)/338

    tan(A-π/4) = (tanA-tan π/4)/(1+tanA tan π/4)
    = (3/4 - 1)/(1 + (3/4)(1))
    = (1/4)/(7/4)
    = 1/7

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  2. the last is -1/7
    But I'm sure you saw my typo ...

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