15/100
15 __ 100
rise/run = tangent 15 degrees rise = tan(15) x 48 = 12.86 inches
It is 6/15.
For tan(180 degrees), this is simply sin(180 degrees)/cos(180 degrees). To find these values, note that 180 degrees is the leftmost point on the unit circle, at y=0, x=-1, so is tan(180 degrees)=0/-1=0. Then adding 15 gives 15.
0.26794919243112270647255365849413
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)
15/8
15/100
15 __ 100
24
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.
rise/run = tangent 15 degrees rise = tan(15) x 48 = 12.86 inches
It is 6/15.
For tan(180 degrees), this is simply sin(180 degrees)/cos(180 degrees). To find these values, note that 180 degrees is the leftmost point on the unit circle, at y=0, x=-1, so is tan(180 degrees)=0/-1=0. Then adding 15 gives 15.
0.2667
they have the same value they're equal