In a right triangle, the sine (sin), cosine (cos), and tangent (tan) of an angle are related by the Pythagorean identity and the quotient identity.

The Pythagorean identity is: sin²𝛼 + cos²𝛼 = 1
The quotient identity is: tan𝛼 = sin𝛼 / cos𝛼

Given that sin𝛼 = 40/41 and tan𝛼 = 40/9, we can use these identities to find cos𝛼.

First, let's rearrange the Pythagorean identity to solve for cos𝛼:

cos²𝛼 = 1 - sin²𝛼
cos²𝛼 = 1 - (40/41)²
cos²𝛼 = 1 - 1600/1681
cos²𝛼 = 81/1681
cos𝛼 = sqrt(81/1681)
cos𝛼 = 9/41

So, the value of cos𝛼 is 9/41.

Question

In a right triangle, the sine (sin), cosine (cos), and tangent (tan) of an angle are related by the Pythagorean identity and the quotient identity.

The Pythagorean identity is: sin²𝛼 + cos²𝛼 = 1
The quotient identity is: tan𝛼 = sin𝛼 / cos𝛼

Given that sin𝛼 = 40/41 and tan𝛼 = 40/9, we can use these identities to find cos𝛼.

First, let's rearrange the Pythagorean identity to solve for cos𝛼:

cos²𝛼 = 1 - sin²𝛼
cos²𝛼 = 1 - (40/41)²
cos²𝛼 = 1 - 1600/1681
cos²𝛼 = 81/1681
cos𝛼 = sqrt(81/1681)
cos𝛼 = 9/41

So, the value of cos𝛼 is 9/41.

Knowee AI · Accepted Answer

In a right triangle, the sine (sin), cosine (cos), and tangent (tan) of an angle are related by the Pythagorean identity and the quotient identity.

The Pythagorean identity is: sin²𝛼 + cos²𝛼 = 1
The quotient identity is: tan𝛼 = sin𝛼 / cos𝛼

Given that sin𝛼 = 40/41 and tan𝛼 = 40/9, we can use these identities to find cos𝛼.

First, let's rearrange the Pythagorean identity to solve for cos𝛼:

cos²𝛼 = 1 - sin²𝛼
cos²𝛼 = 1 - (40/41)²
cos²𝛼 = 1 - 1600/1681
cos²𝛼 = 81/1681
cos𝛼 = sqrt(81/1681)
cos𝛼 = 9/41

So, the value of cos𝛼 is 9/41.

For an angle with measure 𝛼 in a right triangle, 𝑠𝑖𝑛𝛼=4041 and 𝑡𝑎𝑛𝛼=409. What is the value of 𝑐𝑜𝑠𝛼?