If we have an oblique triangle, then we can’t assume these trig ratios will work. Q: Is sohcahtoa only for right triangles? A: Yes, it only applies to right triangles. So how do we remember these three trig ratios and use them to solve for missing sides and angles?įinding Sides and Angles Using Inverse Trig Common Questions Remember the three basic ratios are called Sine, Cosine, and Tangent, and they represent the foundational Trigonometric Ratios, after the Greek word for triangle measurement.Īnd these trigonometric ratios allow us to find missing sides of a right triangle, as well as missing angles. Key Point: Regardless of the size of the triangle, these trigonometric ratios will always hold true for right triangles. Therefore, the sets of ratios depend only on the measure of the acute angle, not the size of the triangle. It stated that the ratios of the lengths of two sides of similar right triangles are equal. We’ll dive further into the theory behind it in the video below, but essentially it’s taken from the AA Similarity Postulate that we learned about previously. It’s a mnemonic device to help you remember the three basic trig ratios used to solve for missing sides and angles in a right triangle.

It’s probably one of the most famous math mnemonics alongside PEMDAS.Īnd it’s an essential technique for your mathematical toolbelt. Periodic Formulas If n is an integer.Jenn, Founder Calcworkshop ®, 15+ Years Experience (Licensed & Certified Teacher) sin (ωθ ) →ġ + cot 2 θ = csc 2 θ Even/Odd Formulas sin ( −θ ) = − sin θ csc ( −θ ) = − cscθ cos ( −θ ) = cos θ So, if ω is a fixed number and θ is any angle we have the following periods.

Period The period of a function is the number, T, such that f (θ + T ) = f (θ ). Hypotenuse opposite hypotenuse sec θ = adjacent adjacent cot θ = opposite csc θ =įacts and Properties Domain The domain is all the values of θ that can be plugged into the function. Tangent and Cotangent Identities sin θ cos θ tan θ = cot θ = cos θ sin θ Reciprocal Identities 1 1 csc θ = sin θ = sin θ csc θ 1 1 sec θ = cos θ = cos θ sec θ 1 1 cot θ = tan θ = tan θ cot θ Pythagorean Identities sin 2 θ + cos 2 θ = 1 yĪdjacent opposite hypotenuse adjacent cos θ = hypotenuse opposite tan θ = adjacent Unit circle definition For this definition θ is any angle. Trig Cheat Sheet Definition of the Trig Functions Right triangle definition For this definition we assume that 0 <θ <

Gre trig cheat sheet