Mathematics: Given tan(a) = 2 and a is in quadrant i, find sin(2a) and find cos(2a). 0 1 1/2 4/5 0 1 1/2 -3/5

Given tan(a) = 2 and a is in quadrant i, find sin(2a)

Ответ:

jkemail19

13.03.2022

We can use following formula

$tan^{2}(A) = \frac{1- cos(2A)}{1+cos(2A)} 
\\ \\ tan(A) =2, so
\\ \\4= \frac{1- cos(2A)}{1+cos(2A)} 
\\ \\1-cos(2A)=4+4cos(2A) 
\\ \\ 5cos(2A) = -3
\\ \\ cos (2A) = -3/5$

Now, we need to find sin(2A).

$sin^{2}(2A) + cos^{2}(2A) = 1
\\ \\ sin^{2}(2A) + (- \frac{3}{5})^{2} =1
\\ \\ sin^{2}(2A) =1 - \frac{9}{25} 
\\ \\ sin^{2}(2A) = \frac{16}{25} 
\\ \\ sin(2A) = \frac{4}{5} \ or \ - \frac{4}{5}$

Because, the angle A is in the 1st quadrant, and cos(2A) is negative, that means that the angle 2A is in the 2nd quadrant and sin(2A) is a positive number,so sin(2A) = 4/5.

sin(2A) = 4/5
cos(2A) = -3/5

0,0(0 оценок)

Ответ:

sleepypizza

14.02.2023

Mathematics

Step-by-step explanation:

0,0(0 оценок)

Given tan(a) = 2 and a is in quadrant i, find sin(2a) and find cos(2a). 0 1 1/2 4/5 0 1 1/2 -3/5

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question