Summary Trigonometry Word Notes (with Word Problems)
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Course
Trigonometry
Institution
The document provides an overview of trigonometry, a branch of mathematics that studies the relationships between angles and sides of triangles. It highlights several important concepts and applications of trigonometry, including trigonometric ratios, SOHCAHTOA, the unit circle, Pythagorean theorem...
Trigonometry Notes
● Trigonometric ratios: Trigonometric ratios are the ratios of the sides of a right triangle to
its angles. The three basic trigonometric ratios are sine (sin), cosine (cos), and tangent
(tan).
● SOHCAHTOA: SOHCAHTOA is a mnemonic that can be used to remember the
trigonometric ratios. SOH stands for "sine equals opposite over hypotenuse," CAH
stands for "cosine equals adjacent over hypotenuse," and TOA stands for "tangent
equals opposite over adjacent."
● Unit circle: The unit circle is a circle with a radius of 1 that is centered at the origin of a
coordinate plane. It is used to define trigonometric functions for angles beyond 90
degrees.
● Pythagorean theorem: The Pythagorean theorem 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.
● Inverse trigonometric functions: Inverse trigonometric functions are used to find the
angle that corresponds to a given trigonometric ratio. The inverse sine function is
denoted as sin⁻¹, the inverse cosine function is denoted as cos⁻¹, and the inverse tangent
function is denoted as tan⁻¹.
● Trigonometric identities: Trigonometric identities are equations that are true for all values
of the variables involved. Some important trigonometric identities include the
Pythagorean identity (sin²θ + cos²θ = 1), the reciprocal identities (cscθ = 1/sinθ, secθ =
1/cosθ, and cotθ = 1/tanθ), and the quotient identity (tanθ = sinθ/cosθ).
● Applications: Trigonometry has many real-world applications, including in navigation,
surveying, and physics. For example, trigonometry can be used to determine the height
of a tall building, the distance between two points, or the trajectory of a projectile.
(next page contains word problems for trigonometry along with answer key)
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