Trigonometry

Periodically

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 values of tan are limitless (that is to say, within [-inf, inf]). However, sin and cos ratios are between -1 and 1. Think about it: sin = opposite/hypotenuse. Since hypotenuse is always larger than or equal to opposite, sin must always be less than 1. Same with cos.

cos(37 deg) = 0.7986

sin(48 deg) = 0.7431 (approx).

Every multiple of 180 degrees, beginning with zero.

This stands for side-side-side. It means if two triangles have three sides that are the same length, than they triangles are congruent.

sin/cos

The INV button is the same as the SHIFT button on the top left corner of the buttons (the leftmost button under the screen).

tan(-60 degrees) = - sqrt(3)

Triangles with three equal sides are called equilateral triangles.

The easiest way of calculating this is to find the probability that all three are boys, as this is the only arrangement that does not fit the criteria. Then work out the answer by taking this away from 1. Probability that all three are boys = 1/2 x 1/2 x 1/2 = 1/8. probability of there being at least one girl is 1 - 1/8 = 7/8 or 87.5%

sin(theta) = 15/17, cosec(theta) = 17/15

cos(theta) = -8/17, sec(theta) = -17/8

cotan(theta) = -8/15

theta = 2.0608 radians.

Just as at 90 degrees, it goes to infinity. That is because tangent of angle is opposite side over adjacent side. The oppsoite side gets bigger and bigger after 45 dgerees ( and in your case then after 225 degrees) until it grows beyond all bounds at 270 degrees

-1

sin2x / (1-cos x) = (1-cos2x) / (1-cos x) = (1-cos x)(1+cos x) / (1-cos x) = (1+cos x)

sin2x=1-cos2x as sin2x+cos2x=1

1-cos2x = (1-cos x)(1+cos x) as a2-b2=(a-b)(a+b)

The radical answer is sqrt(3)/2.

(0.86602540378443864676372317075294)

I was wondering if you knew but I think sophomore or junior. I was two grade levels ahead in math so I don't know for sure.

It is trigonometry.

It is approx 0.9725

This may not be the most efficient method but ...

Let the three angle be A, B and C.

Then note that A + B + C = 20+32+38 = 90

so that C = 90-A+B.

Therefore,

sin(C) = sin[(90-(A+B) = cos(A+B)

and cos(C) = cos[(90-(A+B) = sin(A+B).

So that tan(C) = sin(C)/cos(C) = cos(A+B) / sin(A+B) = cot(A+B)

Now, tan(A+B) = [tan(A)+tan(B)] / [1- tan(A)*tan(B)]

so cot(A+B) = [1- tan(A)*tan(B)] / [tan(A)+tan(B)]

The given expressin is

tan(A)*tan(B) + tan(B)*tan(C) + tan(C)*tan(A)

= tan(A)*tan(B) + [tan(B) + tan(A)]*cot(A+B)

substituting for cot(A+B) gives

= tan(A)*tan(B) + [tan(B) + tan(A)]*[1- tan(A)*tan(B)]/[tan(A)+tan(B)]

cancelling [tan(B) + tan(A)] and [tan(A) + tan(B)], which are equal, in the second expression.

= tan(A)*tan(B) + [1- tan(A)*tan(B)]

= 1

Cotangent is 1 / tangent.

Since tangent is sine / cosine, cotangent is cosine / sine.

Inverse sine is defined for the domain [-1, 1]. Since 833 is way outside this domain, the value is not defined.

-1273 degrees lies in quadrant two. Simply add 360 degrees repeatedly until it becomes positive, giving 167 degrees. Note that is greater than 90 and less than 180, making it quadrant two.

A useful property in Trigonometry is:

tan(x) = sin(x) / cos(x)

So, cos(x) tan(x) = cos(x) [ sin(x) / cos (x)]

= sin(x)