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Omni-MATH / Alex picks his favorite point (x,y) in the first quadrant on the unit circle x²+y²=1, such that a ray from the origin through (x,y) is θ radians counterclockwise from the positive …

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problem

Alex picks his favorite point (x,y)(x, y) in the first quadrant on the unit circle x2+y2=1x^{2}+y^{2}=1, such that a ray from the origin through (x,y)(x, y) is θ\theta radians counterclockwise from the positive xx-axis. He then computes cos−1(4x+3y5)\cos ^{-1}\left(\frac{4 x+3 y}{5}\right) and is surprised to get θ\theta. What is tan(θ)\tan (\theta)?
Plain-text mathematical notation (without MathML)
Alex picks his favorite point (x,y) in the first quadrant on the unit circle x²+y²=1, such that a ray from the origin through (x,y) is θ radians counterclockwise from the positive x-axis. He then computes cos^(−1)((4x+3y)/(5)) and is surprised to get θ. What is tan(θ)?
Original LaTeX notation
Alex picks his favorite point $(x, y)$ in the first quadrant on the unit circle $x^{2}+y^{2}=1$, such that a ray from the origin through $(x, y)$ is $\theta$ radians counterclockwise from the positive $x$-axis. He then computes $\cos ^{-1}\left(\frac{4 x+3 y}{5}\right)$ and is surprised to get $\theta$. What is $\tan (\theta)$?

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Source and history

task_id
e8a1490c-0347-54cb-a3e9-ae17c9afcbc0
task_key
test--e8a1490c-0347-54cb-a3e9-ae17c9afcbc0
task_revision_id
1
config / split
/ test

Official source

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