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Excel in math and science
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Trigonometric Functions
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Concept Quizzes
\( \theta\) is an acute angle such that \(\tan (\theta) = \frac{1}{3}\). What is the value of \(10 \sqrt{10}\cdot\left(\sin \theta + \cos \theta \right)\)?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Let \(m\) and \(M\) be the minimum and maximum values of the domain of \(f(x) = \sin^{-1}(x^2 - 360)\), respectively. What is the value of \(M - m\)?
Details and assumptions
\(\sin^{-1} x\) denotes the functional inverse of \(\sin x\) not the reciprocal \(\frac{1}{\sin x}.\)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
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Our wiki is made for math and science
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Let \(O\) be the origin and \(P\) be a point in the fourth quadrant on the x-y plane. Let \(270 ^\circ < \theta < 360^\circ \) be the angle formed by \(OP\) with the positive x-axis. Similarly \(Q\) is a point in the fourth quadrant on the x-y plane where \(|OQ| = |OP|\) and the angle formed by \(OQ\) and the x-axis is \(7\theta\). For what value of \(\theta\) does the segments \(OP\) and \(OQ\) coincide?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
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Let \(\theta\) be the angle between the x-axis and the line connecting the origin \(O (0,0)\) and the point \(P (-8,-15)\), where \(180^\circ < \theta < 270^\circ\). Given that \(\sin \theta + \cos \theta + \tan \theta = \frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?