Question

part 1. Find the value of the trig function indicated, use the Pythagorean Theorem to find the 3rd side if you need it​

Answer 1

Answer:
`\bold {1)\ \cos\ \theta}=(\sqrt2)/(2)\qquad 2)\ \tan \theta =(1)/(3)\qquad 3)\ \cos\ \theta=(3√(13))/(13)\qquad 4)\ \cos\ \theta = (2\sqrt5)/(5)}`

Explanation:

Pythagorean Theorem is: a² + b² = c², where "c" is the hypotenuse

`1)\ \cos \theta=\frac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=(2)/(2\sqrt2)\quad =\large\boxed{(\sqrt2)/(2)}`

Note: 2² + 2² = hypotenuse² → hypotenuse = 2√2

`2)\ \tan \theta=\frac{\text{side opposite to}\ \theta}{\text{side adjacent to}\ \theta}=(2)/(2\sqrt2)\quad =(5)/(15)\quad \rightarrow \large\boxed{(1)/(3)}`

Note: hypotenuse not needed for tan θ

`3)\ \cos \theta=\frac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=(3)/(√(13))\quad =\large\boxed{(3√(13))/(13)}`

Note: 2² + 3² = hypotenuse² → hypotenuse = √13

`4)\ \cos \theta=\frac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=(4)/(2\sqrt5)\quad =\large\boxed{(2\sqrt5)/(5)}`

Note: hypotenuse given in problem