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ohhnana
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Homework Statement
cos x is a first quadrant angle in standard position and cos x =1/√10 . Find the exact value of sin .
Homework Equations
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The Attempt at a Solution
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Excerpt from the forum rules (https://www.physicsforums.com/showthread.php?t=414380)ohhnana said:Homework Statement
cos x is a first quadrant angle in standard position and cos x =1/√10 . Find the exact value of sin .
Homework Equations
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The Attempt at a Solution
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The equation sin x = √1 - (1/√10)^2 represents a trigonometric identity that relates the sine function to the cosine function. It is commonly known as the Pythagorean identity.
The equation sin x = √1 - (1/√10)^2 is derived from the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is represented by 1, and the other two sides are represented by 1/√10 and √1.
Yes, the equation can be graphed on a coordinate plane. The graph will show a sinusoidal curve with an amplitude of 1 and a period of 2π. The curve will also intersect the x-axis at points where sin x = 0, which are located at x = 0, π, 2π, etc.
The equation sin x = √1 - (1/√10)^2 is used in various fields, such as physics, engineering, and astronomy. It is used to model periodic phenomena and to solve problems involving periodic motion, such as the motion of pendulums and waves.
Yes, there are other variations of the Pythagorean identity, such as cos x = √1 - sin^2 x and tan x = sin x/cos x. These identities are all derived from the Pythagorean theorem and are fundamental concepts in trigonometry.