Express x and y in terms of trigonometric ratios, express your answer in terms of theta only.

Solution:

From the figure, it is a right angled triangle

All trigonometric ratios can be applied here

The length of adjacent side to the angle θ is 6cm

The length of opposite side to the angle θ is x and hypotenuse is y

tan(θ) value is the ratio of the side which is opposite to the angle θ and the adjacent side to the angle θ.

tan(θ) = opposite side to angle θ/ adjacent side to angle θ

tan(θ) = x/6

x = 6 tan(θ)

Therefore, x value in terms of trigonometric ratios is x = 6 tan(θ).

cos(θ) value is the ratio of side which is adjacent to the angle θ and the hypotenuse of the right angled triangle.

cos(θ) = adjacent side to angle θ/ hypotenuse

cos(θ) = 6/y

y = 6/ cos(θ)

y = 6 sec(θ)

Therefore, the values of x and y are tan(θ) and sec(θ).

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Express x and y in terms of trigonometric ratios, express your answer in terms of theta only.

Summary:

Expressing x and y in terms of trigonometric ratios is x = tan(θ) and y = sec(θ).