Answer:
[tex](1)sin\: \theta =\dfrac{4}{5} \\\\(2)tan\: \theta =\dfrac{4}{3}\\\\(3)cosec\: \theta =\dfrac{5}{4}\\\\(4)sec\: \theta =\dfrac{5}{3}\\\\(5)cot\: \theta =\dfrac{3}{4}[/tex]
Step-by-step explanation:
If Cos A[tex]=\frac{3}{5}[/tex]
Recall that:
[tex]cos \theta =\frac{Adjacent}{Hypotenuse} \\$Therefore:\\Adjacent=3\\Hypotenuse=5[/tex]
By knowledge of Pythagorean Triples, we know that the Opposite of A=4.
[tex](1)sin\: \theta =\dfrac{Opposite}{Hypotenuse}=\dfrac{4}{5} \\\\(2)tan\: \theta =\dfrac{Opposite}{Adjacent}=\dfrac{4}{3}\\\\(3)cosec\: \theta =\dfrac{1}{sin\theta}=\dfrac{5}{4}\\\\(4)sec\: \theta =\dfrac{1}{cos\theta}=\dfrac{5}{3}\\\\(5)cot\: \theta =\dfrac{1}{tan\theta}=\dfrac{3}{4}[/tex]
