1.

When drawn in standard position, an angle ø has a terminal ray that lies In the second quadrant and whose sine is equal to 9/41. Find the exact value of cos ø and tan ø

Answer»

values of cosθ = -40/41 and tanθ = -9/40

It is given that θ is an angle which is made by a ray in SECOND QUADRANT whose sine is EQUAL to 9/41.

        i.e., sinθ = 9/41 = perpendicular/hypotenuse

so, perpendicular = 9 and hypotenuse = 41

then, base = √{hypotenuse² - perpendicular²}

        = √{41² - 9²} = 40

so, cosθ = base/hypotenuse = 40/41

but θ is in second quadrant so, cosθ = -40/41

now tanθ = perpendicular/base = 9/40

tangent is negative in second quadrant.

so, tanθ = -9/40


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