Hello. Thanks for any help in advance. just having trouble with the method of eliminating θ from the following pairs of equations: a. x = 2 cosθ, y = 2 sin θ b. x = b tan, y = a sec θ
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Originally Posted by shimmerblade Hello. Thanks for any help in advance. just having trouble with the method of eliminating θ from the following pairs of equations: a. x = 2 cosθ, y = 2 sin θ b. x = b tan, y = a sec θ The key is to use the many forms of the Pythagorean Identity - in this case and . (a) . Can you follow a similar process for (b)?
for b. x = b tan θ, y = a sec θ would it be something like (b tan θ)^2 + 1 = (a sec θ)^2 b^2 tan^2 θ + b^2 a^2 = a^2 sec^2 θ b^2 (tan^2 θ + a^2)^2 = a^2 (sec^2 θ) b^2 x^2 + a^2 b^2 = a^2 y^2 not too sure....=\
Originally Posted by shimmerblade for b. x = b tan θ, y = a sec θ would it be something like (b tan θ)^2 + 1 = (a sec θ)^2 b^2 tan^2 θ + b^2 a^2 = a^2 sec^2 θ b^2 (tan^2 θ + a^2)^2 = a^2 (sec^2 θ) b^2 x^2 + a^2 b^2 = a^2 y^2 not too sure....=\ You're on the right track. Remember that , so . If then . .
ok thanks for your help.
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