Q: What does Tan 3 theta equals -1?

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If tan theta equals 2, then the sides of the triangle could be -2, -1, and square root of 5 (I used the Pythagorean Theorem to get this). From this, sec theta is negative square root of 5. It is negative because theta is in the third quadrant, where cosine, secant, sine, and cosecant are all negative.

3cot(A) = 4 so cot(A) = 4/3 then tan(A) = 1/(4/3) = 3/4 and so 1 - tan(A) = 1-3/4 = 1/4

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.

If the angles are measured in degrees or gradians, then: tan 3 > tan 2 > tan 1 If the angles are measured in radians, then: tan 1 > tan 3 > tan 2.

3cos(y) = 3/(sqrt(1+x^2)

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Cotan(theta) is the reciprocal of the tan(theta). So, cot(theta) = 1/2.

0.75

tan3A-sqrt3=0 tan3A=sqrt3 3A=tan^-1(sqrt3) 3A= pi/3+npi A=pi/9+npi/3 n=any integer

If tan theta equals 2, then the sides of the triangle could be -2, -1, and square root of 5 (I used the Pythagorean Theorem to get this). From this, sec theta is negative square root of 5. It is negative because theta is in the third quadrant, where cosine, secant, sine, and cosecant are all negative.

Negative 1.047197551 etc, etc.

tan3theta

The answer is 60 and 240 degrees. Add radical 3 and inverse tan to get answer add 180 for other answer less than 360.

If sin (theta) is 3/5, then sin2 (theta) is (3/5)2, or 9/25.

3cot(A) = 4 so cot(A) = 4/3 then tan(A) = 1/(4/3) = 3/4 and so 1 - tan(A) = 1-3/4 = 1/4

Given that theta is the angle with respect to the positive X axis of a line of length 1, then sin(theta) = Y and cos(theta) is X, with (X,Y) being the point at the end of the line. As theta sweeps from 0 to 360 degrees, or 0 to 2 pi radians, that point draws a circle of radius 1, with center at (0,0).Since X, Y, and 1 form the sides of a right triangle, where 1 is the hypotenuse, then the pythagorean theorem states that X2 + Y2 = 12. This means that sin2(theta) + cos2(theta) = 1.Tan(theta) is defined as sin(theta) divided by cos(theta), or Y / X. Since division by zero is a limiting invalidity, then tan(theta) is asymptotic to Y=0, having value of +infinity at theta = 90 or pi / 4, and -infinity at 270 or 3 pi / 4.

The answer depends on how the ratios are defined. In some cases tan is DEFINED as the ratio of sine and cosine rather than from the angle in a right angled triangle.If the trig ratios were defined in terms of a right angled triangle, thensine is the ratio of the opposite side to the hypotenuse,cosine is the ratio of the adjacent side to the hypotenuse,and tangent is the ratio of the opposite side to the adjacent side.It is then easy to see that sin/cos = (opp/hyp)/(adj/hyp) = opp/adj = tan.If sine and cosine are defined as infinite sums for angles measured in radians, iesin(x) = x - x^3/3! + x^5/5! - x^7/7! + ...andcos = 1 - x^2/2! + x^4/4! - x^6/6! + ...then it is less easy to see tan = sin/cos.

z = 3i r=3 theta=taninverse(3/0)=undefine as we know tan theta is undefine at 90 and 270....check through qustion ..their is + sign with imag part....its mean angle is 90 so we write it as 3(cos90 + isin90)