Trig

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find the exact value of the expression using the provided information. Find Tan (S+T) given that cos s=1/3 with s in quad I and sin T= -1/2 with T in quad IV

  • Trig -

    s is in Q1 (sin>0, cos>0)
    so
    cos(s)=1/3,
    sin(s)=+√(1-(1/3)²)
    =√(8/9)
    tan(s)=√(8/9) / (1/3)
    =√8

    t is in Q4 (sin<0, cos>0)
    sin(t)=-1/2
    cos(t)=+√(1-(1/2)²)
    =√(3/4)
    tan(t)=(-1/2)/√(3/4)
    =-1/√3
    [rationalize by multiplying numerator and denominator by √3]
    =-(√3)/3

    Use the identity
    tan(s+t)=(tan(s)+tan(t))/(1-tan(s)tan(t)) to calculate tan(s+t)
    I get about 0.85.

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