Pythagorean Identity!

Question

Please help!

 

Use the Pythagorean Identity Sin^2 t +Cos^2 t =1 and give information to find Cos t

 

Sin t = 2 Square root 2/ 3; 0 Less than or equal to T less then pi/2.

 

 

Answer Given Are

 

A. 1/3 .    B. 2/square root 2.      C. 2/3.      D. 3 square root2/4

Answer 1

Using the Pythagorean Identity sin^2 ⁡t + cos^2 ⁡t = 1 , find cos ⁡t given:

sin ⁡t = (2√2)/3

0 ≤ t < π/2

STEP 1: FIND sin^2 ⁡t

sin^2⁡ t = ( (2√2)/3)^2 = (2√2)/3∙(2√2)/3 = (4∙2)/9 = 8/9

STEP 2: SUBSTITUTE VALUE FOR sin^2 ⁡t AND SOLVE

8/9 + cos^2⁡ t =1

cos^2⁡ t = 1-8/9

cos^2⁡ t = 1/9

√(cos^2 ⁡t )=√(1/9)

cos⁡ t = ±1/3

Since 0 ≤ t < π/2 , cos⁡ t = 1/3

ANSWER CHOICE: A