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 :

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

[tex]=\frac{-2}{\sqrt[]{5}}[/tex]

Rationalize

[tex]=-\frac{2\sqrt[]{5}}{5}[/tex]

cosθ = adj / hyp

[tex]=\frac{-1}{\sqrt[]{5}}[/tex]

rationalize

[tex]=-\frac{\sqrt[]{5}}{5}[/tex]

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