Find the exact value of tan (240)?
tan (240) = sin(240) / cos(240) = (-sqrt(3)/2) / (-1/2) = sqrt(3)
Find the exact value of tan^-1 sqrt(3)?
Remember that tangent is sine over cosine. This means one fraction divided by another will give √(3) When you divide a fraction by a fraction, you flip the second fraction. Since the result is √(3), you know that √(3) is in the numerator of the problem. That indicates the use of √(3)/2 as the first value. It indicates the first one because if it were the second one, it would be flipped and become 1/√(3). Since tangent is sine over cosine, think of when sine is √(3)/2: sin( π/3 ) = sin( 60° ) = √(3)/2 And cosine there is: cos( π/3 ) = cos( 60° ) = 1/2 Thus tangent is: tan( π/3 ) = tan( 60° ) = sin( 60° )/cos( 60° ) = [ √(3)/2 ] / [ 1/2 ] = [ √(3)/2 ] × [ 2/1 ] = [ √(3)/1 ] × [ 1/1 ] = √(3) ---- The exact value is π/3 radians or 60°. ---- If you need arctangent of 1/√(3) then you would know that the flipped fraction had √(3) and look for when cosine is √(3)/2.
What is the exact value of tan (5pi/6)?
here are the choices: a. square root of three all over three b. negative square root of three all over three c. 1/2 d. negative square root of 2 all over 2 thank you.. please have a brief explanation.. ^_^
What is the exact value of tan 330? Would (-1/sqrt3) work?
Yes. Because of where it is on the unit circle, 330 degrees is the fourth quadrant location of 30 degrees. 330 degrees is the coordinate (√3/2, -1/2). Tangent is y / x , or (-1/2) / (√3 / 2). which is (-1 / √3) But most people write it so that no squareroots are on the denominator. so it would be -√3 / 3
Help - Find Exact Value of Tan(11PI/6)?
tan(11pi/6) = -tan(pi/6) = -1/sqrt(3) = -sqrt(3)/3 Use the fact that the sides of a 30-60-90 triangle are in the ratio 1-sqrt(3)-2. pi/6 radians = 30 degrees The opposite side of the 30 degree angle is 1. The adjacent side of a 30 degree angle is sqrt(3). tan(30) = opp/adj = 1/sqrt(3) Remember that 11pi/6 is in the fourth quadrant and tangent is negative there.
What is the value of tan 15°?
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Find the exact value of tan^-1((-sqrt(3)/3)) in terms of pi?
OK--- There are two answers to your question in the 0 to 2pi interval. The first would be 5pi/6 since Q2 has sin as + and cos as -. The second would be -pi/6 or 11pi/6 since sin is - and cos is + in Q4. You can add 2pi, 4pi,6pi..etc..to either of these answers to get a multitude of answers. You didn't specify an interval.
What is the value of tan 135°?
Because sine, cosine, and tangent arefunctions (trig functions), they can be defined as even or odd functions as well. Sine and tangent are both odd functions, and cosine is an even function. In other words, sin(–x) = –sin x.Since Tan is an odd function, when tan (135) = tan (90+45) or even tan (180–45) this both yeilds the same result,For tan(90+45), it is equivalent to -cot(45) hence as we know tan(45) or cot (45) is always equal to 1, we will get answer as -1Similarly, tan(180–45),It will remain tan only as it is function of π but the sign will matter, as this 135 degree lies in quadrant 2, the sign of x coordinate is always negative, hence the outcome will always be negative. As tan(-x) = -tan(x)So tan(180–45) will also yeild to -tan45And as tan 45 = 1 and -tan45 = -1So the answer to this question, i.e. tan135 is always equal to -1
What is the exact value of tan(arctan3/4-arcsin1/2)?
a = arctan 3/4 tan a = 3/4 b = arcsin 1/2 sin b = 1/2 tan b = 1/sqrt(3) tan (arctan 3/4-arcsin 1/2) = tan (a - b) = (tan a - tan b) / (1 + tan a tan b) = (3/4 - 1/sqrt(3)) / (1+ (3/4)(1/sqrt(3))) = (3sqrt(3) - 4) / (4sqrt(3) + 3)