Question

Find the value of cosine theta​, given that sine theta equals 0.7296​, if theta is an acute angle. ​(Round to four decimal places as​ needed.)cos theta = ?

Answer 1

The value of cos(theta) is approximately 0.6844.

Step-by-step explanation:

To find the value of cos(theta) given that sin(theta) equals 0.7296, we can use the Pythagorean identity for sine and cosine in a right-angled triangle. The Pythagorean identity is given by sin^2(theta) + cos^2(theta) = 1. Since theta is an acute angle, we know that cos(theta) is positive.

Given sin(theta) = 0.7296, we can substitute this into the Pythagorean identity:

`\[0.7296^2 + \cos^2(\theta) = 1.\]`

Solving for cos^2(theta):

`\[\cos^2(\theta) = 1 - 0.7296^2,\]`

`\[\cos^2(\theta) = 1 - 0.5329,\]`

`\[\cos^2(\theta) = 0.4671.\]`

Taking the square root of both sides, remembering that cos(theta) is positive:

`\[\cos(\theta) = √(0.4671).\]`

Therefore,
`\(\cos(\theta)\)` is approximately 0.6844 when rounded to four decimal places.

In summary, by applying the Pythagorean identity and solving for cos(theta), we find that the value of cos(theta) is approximately 0.6844 when sine theta is given as 0.7296 for an acute angle theta.