Q. 77 - Precalculus Enhanced with Graphing Utilities

Question

Use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator.

${\sin }^2{40}^{\mathrm{o}}+{\cos }^2{40}^{\mathrm{o}}$

Step-by-Step Solution

Answer

The exact value of trigonometry expression is $1.$

Step 1. Given Information

Given that the expression is ${\sin }^2{40}^{\mathrm{o}}+{\cos }^2{40}^{\mathrm{o}}.$ To find the exact value of given expression using Pythagorean identity.

Step 2. Using Pythagorean identity

The Pythagorean identity can be denoted as,

${\sin }^2\mathrm{\theta }+{\cos }^2\mathrm{\theta }=1$

On substituting $\mathrm{\theta }={40}^{\mathrm{o}},$

${\sin }^2{40}^{\mathrm{o}}+{\cos }^2{40}^{\mathrm{o}}=1$