Question

GRAPHS Suppose the terminal side of an angle θ in standard position coincides with the graph of y = 2x in Quadrant III. Find the six trigonometric functions of θ.

Answer 1

y = 2x

Comparing y=mx + b

m = 2

The y-intercet and x -intercept is at (0,0)

Find the hypotenuse using pythagoras theorem

hypotenuse² = adj² + opp²

= (-1)² + (-2)²

= 1 + 4

= 5

hypotenuse =√5

The six trigonometric values can be determined by applying the trigonometric ratio

sinθ = opp/ hyp

`=\frac{-2}{\sqrt[]{5}}`

Rationalize

`=-\frac{2\sqrt[]{5}}{5}`

cosθ = adj / hyp

`=\frac{-1}{\sqrt[]{5}}`

rationalize

`=-\frac{\sqrt[]{5}}{5}`