Question

Consider the following by looking at the website below.
www.webassign.net/waplots/3/a/808112f7e2262ae957c47b37497635.gif
a) Find the length of the third side of the triangle in terms of x.
b)Find θ in terms of x for all three inverse trigonometric functions.(θ=sin^−1, θ=cos^−1, and θ=tan^−1)

Answer 1

Use the Pythagorean theorem that will help you with A

Answer 2

thanks, what do i do for b?

Answer 3

Use the Pythagorean identity and if that does not work try the reciprocal identity.

Answer 4

the 3rd side is y=√(49-x^2)
Now just use the normal ratios to find the trig values.
sinθ = x/7
cosθ = y/7 = √(49-x^2)/7
tanθ = x/y = x/√(49-x^2)

that means that
θ = sin^{^-1} x/7
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