Find the exact value of COSG ir cosa and COS 4 if the ter

Find the exact value of COSG+ ) ir cosa- and COS = 4 , if the terminal side of lies in quadrant TV and the terminal side of liesin cos( + ) = 2 Edit

Solution:

Cos() = 11/61 and cos() = 9/41

Cos (+) = cos.cos – sin.sin

We know; sin²(x) + cos²(x) = 1 => sin(x) = sqrt(1 - cos²(x))

Since, Cos() = 11/61 then Sin() = ±(1 - (11/61)²) = ± 60/61

is in quadrant IV, So Sin() = - 60/61

Since, Cos() = 9/41 then Sin() = ±(1 - (9/41)²) = ± 40/41

is in quadrant I, So Sin() = 40/41

Cos (+) = cos.cos – sin.sin

= (11/61) (9/41) - (-60/61) (40/41)

= 99/2501 + 2400/2501

Cos (+) = 2499 / 2501 = 0.9992