Express x and y in terms of trigonometric ratios of θ. (express your answer in terms of θ only.)

Asked by maham237 @ 02/12/2020 in Mathematics viewed by 367 People

Answered by maham237 @ 02/12/2020

Here you'll just be using the SOH CAH TOA thing (or that's the way i learned it), so

sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent

so x, in relation to theta, is the OPPOSITE of the angle and ADJACENT to 6. because you're using opp and adj, you'll use tangent.

tan(theta) = (x/6)

but, because the answer calls for x to be isolated, it'll look like:

x = 6 tan (theta)

all you do is get x alone.

y is the HYPOTENUSE of the right triangle, so you can use either sine or cosine with it. I'll use cos, so it'll be using 6 (the adjacent) and the hypotenuse, aka Y

cos(theta) = (6/y)

then get y alone

y cos (theta) = 6
y = (6/costheta)

Express x and y in terms of trigonometric ratios of θ. (express your answer in terms of θ only.)

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