Explanation Formula used: Trigonometry ratios: sin θ = Opposite Hypotenuse , csc θ = Hypotenuse Opposite , cos θ = Adjacent Hypotenuse , sec θ = Hypotenuse Adjacent tan θ = Opposite Adjacent and cot θ = Adjacent Opposite . Theorem used: Pythagoras theorem: For a right triangle ABC , ( hypotenuse ) 2 = ( base ) 2 + ( opposite side ) 2 . Calculation: Consider a right triangle ABC with an angle 30 ° where C is the midpoint of the base BD of an equilateral triangle ABD with side length 2 units. The right triangle is as shown below in Figure 1. From Figure 1, it is observed that the hypotenuse and opposite side of the angle 30 ° are 2 and 1 respectively

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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Chapter 8.1, Problem 17E

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To find: The exact value of sec30° without the use of a calculator.

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Chapter 8.1, Problem 16E

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The exact value of sec 30 ° without the use of a calculator.

Solution Summary: The author explains how to find the exact value of mathrmsec30° without the use of a calculator.

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