Question

If cos Θ = negative 4 over 7, what are the values of sin Θ and tan Θ? sin Θ = ±square root 33 over 7; tan Θ = ±square root 33 over 4 sin Θ = ±3 over 7; tan Θ = ±square root 33 sin Θ = ±33 over 7; tan Θ = ±square root 33 over 7 sin Θ = ±square root 33 over 7; tan Θ = ±square root 33 over 7

Answer 1

we have that\
cos Θ=-4/7

we know that
cos² Θ+sin² Θ=1----------> sin² Θ=1-cos² Θ
sin² Θ=1-(-4/7)²------> 1-16/49-----> 33/49
sin² Θ=33/49---------> sin Θ=±(√33)/7

tan Θ=sin Θ/cos Θ-------> [±(√33)/7]/[-4/7]----> ±(√33)/4

the answer is
sin Θ = ±square root 33 over 7; tan Θ = ±square root 33 over 4