Chapter 6: Q. 60 (page 396)

Use the even–odd properties to find the exact value of each expression. Do not use a calculator.
$\cos (- 30^{o})$

Short Answer

Expert verified

The exact value of the function is $\frac{\sqrt{3}}{2} .$

Step by step solution

Step 1. Given Information

Given that the trigonometric function is $\cos (- 30^{o}) .$ To find the exact value of trigonometric function using even odd property.

Step 2. Even odd property

Cosine function is an even function

$\cos (- θ) = cosθ \cos (- 30^{o}) = \cos (30^{o}) = \frac{\sqrt{3}}{2}$

Step 3. Proof for equilateral triangle

On taking equilateral triangle,

Step 4. Proof using equilateral triangle

On taking the equilateral triangle as ABC and draw a line bisects of A. On taking triangle as $ADC, ∠ CAD = 30^{o}$ . On using Pythagorean triangle,

${AC}^{2} = {AD}^{2} + {DC}^{2} a^{2} = \frac{a^{2}}{4} + {AD}^{2} AD = \frac{\sqrt{3}}{2} a \cos (30^{o}) = \frac{AD}{AC} \cos (30^{o}) = \frac{\frac{\sqrt{3}}{2} a}{a} \cos (30^{o}) = \frac{\sqrt{3}}{2}$

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Use the even–odd properties to find the exact value of each expression. Do not use a calculator.
$\cos (- 30^{o})$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Even odd property

Step 3. Proof for equilateral triangle

Step 4. Proof using equilateral triangle

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Use the even–odd properties to find the exact value of each expression. Do not use a calculator.cos(-30o)

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Even odd property

Step 3. Proof for equilateral triangle

Step 4. Proof using equilateral triangle

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Discrete Mathematics

Logic and Functions

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Use the even–odd properties to find the exact value of each expression. Do not use a calculator.
$\cos (- 30^{o})$