Given that sin𝛼 = 180/181 and tan𝛼 = 180/19, we can find cos𝛼 using the identity sin^2𝛼 + cos^2𝛼 = 1.

First, square the given sin𝛼 to get sin^2𝛼 = (180/181)^2 = 32400/32761.

Then, subtract this from 1 to find cos^2𝛼 = 1 - 32400/32761 = 361/32761.

Finally, take the square root of this to find cos𝛼. Since cos𝛼 is the adjacent/hypotenuse in a right triangle and the adjacent side cannot be longer than the hypotenuse, cos𝛼 must be positive. So, cos𝛼 = sqrt(361/32761) = 19/181.

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Given that sin𝛼 = 180/181 and tan𝛼 = 180/19, we can find cos𝛼 using the identity sin^2𝛼 + cos^2𝛼 = 1.

First, square the given sin𝛼 to get sin^2𝛼 = (180/181)^2 = 32400/32761.

Then, subtract this from 1 to find cos^2𝛼 = 1 - 32400/32761 = 361/32761.

Finally, take the square root of this to find cos𝛼. Since cos𝛼 is the adjacent/hypotenuse in a right triangle and the adjacent side cannot be longer than the hypotenuse, cos𝛼 must be positive. So, cos𝛼 = sqrt(361/32761) = 19/181.

Knowee AI · Accepted Answer

Given that sin𝛼 = 180/181 and tan𝛼 = 180/19, we can find cos𝛼 using the identity sin^2𝛼 + cos^2𝛼 = 1.

First, square the given sin𝛼 to get sin^2𝛼 = (180/181)^2 = 32400/32761.

Then, subtract this from 1 to find cos^2𝛼 = 1 - 32400/32761 = 361/32761.

Finally, take the square root of this to find cos𝛼. Since cos𝛼 is the adjacent/hypotenuse in a right triangle and the adjacent side cannot be longer than the hypotenuse, cos𝛼 must be positive. So, cos𝛼 = sqrt(361/32761) = 19/181.

For an angle with measure 𝛼 in a right triangle, 𝑠𝑖𝑛𝛼=180181 and 𝑡𝑎𝑛𝛼=18019 What is the value of 𝑐𝑜𝑠𝛼 ?

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