if sin theta = 3/5 and cos theta = 4/5, then find tan theta and cot theta
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Answer:
Recall the quotient identity
tan
x
=
sin
x
cos
x
tan
θ
=
sin
x
cos
x
tan
θ
=
3
5
4
5
tan
θ
=
3
5
×
5
4
tan
θ
=
3
4
Note you could have also said that
sin
θ
=
opposite
hypotenuse
,
cos
θ
=
adjacent
hypotenuse
and
tan
θ
=
opposite
adjacent
.
If we know that
sin
θ
=
3
5
, the side opposite
θ
measures 3.
If we know that
cos
θ
=
4
5
, the side adjacent
θ
metres 4.
Applying the definition of
tan
θ
=
opposite
adjacent
, we have that
tan
θ
=
3
4
Hopefully this helps!
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