trigonometry

• The six trigonometric functions are sine, cosine, tangent, cosecant, secant, and cotangent.
• A trigonometric equation is an equation that involves trigonometric functions.
• The Pythagorean Identity states that for any angle θ, sin^2(θ) + cos^2(θ) = 1.
• The graph of the sine function is a smooth, periodic curve that oscillates between -1 and 1.
• The sine of an angle in a right triangle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.
• The sine of an angle in a right triangle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.
• The inverse trigonometric functions are used to find the angle measure given the ratio of sides in a right triangle.
• Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles.
• Trigonometric equations can have multiple solutions.
• The solutions to trigonometric equations are typically given in a specific interval.
• Trigonometric equations can be solved algebraically or graphically.
• Common trigonometric equations include sin(x) = a, cos(x) = b, and tan(x) = c.
• Trigonometric equations can also involve multiple trigonometric functions, such as sin(x) + cos(x) = d.
• The sine function (sin) is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.
• The cosine function (cos) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.
• The tangent function (tan) is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side in a right triangle.
• The cosecant function (csc) is the reciprocal of the sine function, i.e., csc(theta) = 1/sin(theta).
• The secant function (sec) is the reciprocal of the cosine function, i.e., sec(theta) = 1/cos(theta).
• The graph of the cosine function is also a smooth, periodic curve that oscillates between -1 and 1, but it is shifted horizontally by 90 degrees compared to the sine function.
• The period of the sine and cosine functions is 360 degrees or 2π radians.
• The amplitude of the sine and cosine functions is the distance from the midline to the maximum or minimum value, which is always 1.
• The tangent function has vertical asymptotes at odd multiples of 90 degrees or π/2 radians.
• The tangent function has a period of 180 degrees or π radians.
• The cosine of an angle in a right triangle is equal to the length of the side adjacent to the angle divided by the length of the hypotenuse.
• The tangent of an angle in a right triangle is equal to the length of the side opposite the angle divided by the length of the side adjacent to the angle.
• The reciprocal of the sine of an angle is equal to the cosecant of the angle.
• The reciprocal of the cosine of an angle is equal to the secant of the angle.
• The reciprocal of the tangent of an angle is equal to the cotangent of the angle.
• Trigonometric identities can be used to simplify trigonometric equations.
• Trigonometric equations can have no solution or an infinite number of solutions.
• Trigonometric equations are used in various fields such as physics, engineering, and navigation.
• Trigonometric equations can be solved using inverse trigonometric functions.
• The cosine of an angle in a right triangle is equal to the length of the adjacent side divided by the length of the hypotenuse.
• The tangent of an angle in a right triangle is equal to the length of the side opposite the angle divided by the length of the adjacent side.
• The cosecant of an angle in a right triangle is equal to the reciprocal of the sine of the angle.
• The secant of an angle in a right triangle is equal to the reciprocal of the cosine of the angle.
• The cotangent of an angle in a right triangle is equal to the reciprocal of the tangent of the angle.
• The inverse trigonometric functions are denoted as sin^(-1), cos^(-1), tan^(-1), csc^(-1), sec^(-1), and cot^(-1).
• The inverse sine function, sin^(-1)(x), gives the angle whose sine is x.
• The inverse cosine function, cos^(-1)(x), gives the angle whose cosine is x.