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Finding the Values of Basic Trigonometric Functions Here are the definitions for the basic trigonometric functions. Remember that “opposite” means the leg across from the angle of interest, “adjacent” means the leg that makes up one side of the angle of interest, and “hypotenuse” is the side of the triangle opposite the right angle. opposite adjacent opposite sin ϑ = cos ϑ = tan ϑ = hypotenuse hypotenuse adjacent csc ϑ = 1 hypotenuse = sin ϑ opposite sec ϑ = 1 hypotenuse = cos ϑ adjacent cot ϑ = 1 adjacent = tan ϑ opposite Use the formulas above and the Pythagorean Theorem to find the six trigonometric functions for the angles below. 1. 2. sin θ = ________ csc θ = ________ sin θ = ________ csc θ = ________ cos θ = ________ sec θ = ________ cos θ = ________ sec θ = ________ tan θ = ________ cot θ = ________ tan θ = ________ cot θ = ________ 3. 4. sin θ = ________ csc θ = ________ sin θ = ________ csc θ = ________ cos θ = ________ sec θ = ________ cos θ = ________ sec θ = ________ tan θ = ________ cot θ = ________ tan θ = ________ cot θ = ________ 5. 6. sin θ = ________ csc θ = ________ sin θ = ________ csc θ = ________ cos θ = ________ sec θ = ________ cos θ = ________ sec θ = ________ tan θ = ________ cot θ = ________ tan θ = ________ cot θ = ________
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