Question

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

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

Short answer

The exact value of trigonometry expression is$1.$

Step-by-step solution

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

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