How would one solve this problem? find the exact answer: (sin 120)(cos 2pi/3) / tan 315?

Question

the setup of the problem looks like this

(sin 120)(cos 2pi/3)
-------------------------
tan 315

Answer 1

plug them into your calculator in the order they appear.
be sure to switch from radians to degrees where necessary to get .433

Answer 2

you need to know your special triangles: 30-60-90 and 45-45-90 pi/4 = 45 degrees pi/6 = 30 degrees pi/3 = 60 degrees the triangle (and angle) you choose will be based on the acute angle the given angle makes with the x-axis 1) 7pi/4 is the same as -pi/4, or a 45-45-90 triangle in Quadrant 4, where sin is negative and cos is positive sin = y / r = -sqrt(2) / 2 2) cos (-3pi/4) is a 45-45-90 degree triangle in Quadrant 3, where cos and sin are both negative cos (-3pi/4) = -sqrt(2) / 2 3) 7pi/6 is a 30-60-90 triangle in Quadrant 3, with the 30 degree angle at the origin. Since cos and sin are both negative, their quotient (tan) is positive y = -1/2 and x = -sqrt(3) / 2 tan (7pi/6)= y/x = (-1/2) / (-sqrt(3) / 2) = 1 / sqrt(3) = sqrt(3) / 3 it will make your life MUCH easier in trig if you know these special triangles, and their places on the unit circle typically, when looking for the trig values of these angles, you're looking for exact values (sqrt(2) / 2 , not .707; sqrt(3) / 2, not .866)

Answer 3

Are you mixing units? degrees and radians?

Sin 120 degrees = 0.5*SQRT(3)
tan 315 degrees = -1
Cos 2pi/3 radians = cos 120 degrees = - 0.5

0.5 * SQRT(3) * (-0.5) / -1 = 0.25*SQRT(3) = 1.7320508 / 4 = 0.433...

The "exact" answer would be SQRT(3) / 4
(where SQRT(3) means "the square root of 3"

Answer 4

cos(p) / 3 = -0.333333 (or -1/3)