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For example: tan-1(1) = 45 degrees

Q: What is the value of tan 1?

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Any number can be a tan. So -sqrt(17), 19.56, 45678942 are all examples of tan. Cosine can have any value in the range [-1, 1].

1/sqrt(3)

1 because tan(5 pi / 4) = 1

For the tangential value tan θ = 1/2, the angle θ is 26.565° (0.464 radians). The tangent is the opposite side over the adjacent side for an angle, or otherwise sin θ /cos θ.

= tan (48.323 deg) = 1.1232

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tan (pi) / 1 is zero. tan (pi / 1) is zero.

tan(135) = -tan(180-135) = -tan(45) = -1

cot(15)=1/tan(15) Let us find tan(15) tan(15)=tan(45-30) tan(a-b) = (tan(a)-tan(b))/(1+tan(a)tan(b)) tan(45-30)= (tan(45)-tan(30))/(1+tan(45)tan(30)) substitute tan(45)=1 and tan(30)=1/√3 into the equation. tan(45-30) = (1- 1/√3) / (1+1/√3) =(√3-1)/(√3+1) The exact value of cot(15) is the reciprocal of the above which is: (√3+1) /(√3-1)

The value of tan A is not clear from the question.However, sin A = sqrt[tan^2 A /(tan^2 A + 1)]

tan(135 degrees) = negative 1.

1

Any number can be a tan. So -sqrt(17), 19.56, 45678942 are all examples of tan. Cosine can have any value in the range [-1, 1].

To find the exact value of tan 105°. First, of all, we note that sin 105° = cos 15°; and cos 105° = -sin 15°. Thus, tan 105° = -cot 15° = -1 / tan 15°. Using the formula tan(α - β) = (tan α - tan β) / (1 + tan α tan β); and using, also, the familiar values tan 45° = 1, and tan 30° = ½ / (½√3) = 1/√3 = ⅓√3; we have, tan 15° = (1 - ⅓√3) / (1 + ⅓√3); whence, cot 15° = (1 + ⅓√3) / (1 - ⅓√3) = (√3 + 1) / (√3 - 1) {multiplying through by √3} = (√3 + 1)2 / (√3 + 1)(√3 - 1) = (3 + 2√3 + 1) / (3 - 1) = (4 + 2√3) / 2 = 2 + √3. Therefore, tan 105° = -cot 15° = -2 - √3, which is the result we sought. We are asked the exact value of tan 105°, which we gave above. We can test the above result to 9 decimal places, say, by means of a calculator: -2 - √3 = -3.732050808; and tan 105° = -3.732050808; thus indicating that we have probably got the right result.

The value of tan and sin is positive so you must search quadrant that tan and sin value is positive. The only quadrant fill that qualification is Quadrant 1.

1/sqrt(3)

tan u/2 = sin u/1+cos u

The exact value of 60 degrees would be 1/2. This is a math problem.